PHY121

LMPHY121: PHYSICS LABORATORY

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LABORATORY MANUAL



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TABLE OF CONTENTS

TEXTBOOK:

1. LMPHY121.doc

OTHER READINGS: 2. Arora C.L., B.Sc. Practical Physics Chand S. & Company, New Delhi, Twentieth edition, 2007.

Sr. No.

Title of the Experiment Page No.

1 An introduction to units, errors, different types of graphs and measurement of length, mass and time.

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2 To study variation of angular acceleration with torque acting on the fly wheel. Find out the minimum torque required to overcome the friction between the flywheel and bearing and also find out the moment of inertia of the flywheel.

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3 To study the dependence of force of friction on- 1. Normal Reaction 2. Area of contacts 3. Nature of Material 4. Nature of Surface

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4 To plot graph between distance knife edges from the center of gravity and the time period of a compound pendulum.

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5 To determine the value of acceleration due to gravity at a place by Kater's pendulum

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6 To Find the moment of Inertia of an irregular body about an axis passing through its centre of gravity with a torsion pendulum.

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7 To determine the frequency of a electrically maintained tuning fork by using Meldes experiment and hence verify the law of vibrating string

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8 To study one dimensional elastic collision using two hanging sphere. 24

9 To Find the Youngs Modulus of the material of a rectangular bar by bending using traveling Microscope.

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10 To study the induced e.m.f. as the function of velocity of magnet. 29

11 To determine the modulus of rigidity using Maxwell needle. 32


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Experiment 1.

Aim: An introduction to units, errors, different types of graphs and measurement of length, mass and time. Equipment Required: Vernier callipers, screw gauge and multimeter

Material Required: Linear-linear and semi-log graph paper

Learning objective:

(1) Students learn the use of Vernier caliper, screw gauge and multimeter

(ii) Students learn to plot linear-linear and semi-log graphs

Introduction: The precision of length measurements may be increased by using a device that

uses a sliding vernier scale. Two such instruments (identify in the picture above) that are based

on a vernier scale which you will use in the laboratory to measure lengths of objects are the

vernier callipers and the micrometer screw gauge. These instruments have a main scale (in

millimetres) and a sliding or rotating vernier scale.

A multimeter is an electronic measuring instrument that combines several measurement

functions in one unit. A typical multimeter may include features such as the ability to measure

(AC/DC) voltage & current, resistance and testing of a diode.

Zero error occurs when the measuring instrument registered a reading when there should be

none.

Least count of a measuring instrument is the smallest quantity that can be measured accurately

using that instrument. The degree of accuracy of a measurement can be concluded from the

least count of the instrument

Procedure:

Part A (Measurement)

1. To find the density of the given material

You are given a rectangular block and you have to find the density of material of which the

rectangular block is made of. We know density(d) =[mass(m kg)/volume (V m3)].

To find the volume of the rectangular block measure its length, width and height by vernier

caliper.

Take at least five readings of each dimension. Also remember to check and note in your

report sheet the zero error and least count of the vernier caliper you are using. Even if

zero error is zero entry should be recorded in your report sheet. Next measure the mass of the rectangular block using a balance; take at least five readings.

Also note zero error and least count of the balance you use for finding the mass. Tabulate the data, calculate the density along with the possible error.

Error in density(d) d=m/V or d/d= (m/m)+ (V/V) (derive this expression)


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Estimate (m) and (V) to estimate the error (d) in the density you have found out in your experiment.

2. To find the resistivity of a given metal wire

You will need screw gauge and a multimeter for this experiment.

Resistivity (= Resistance(R ohms) [ area of cross-section of the wire (A m

2)/ length of the wire(l m)]

Derive the units of Take a piece of a metal wire of almost uniform cross-section; measure (at leat five times) its

cross section by screw gauge and length (at least five times) by vernier caliper. Measure the

resistance of the above piece of wire using a multimeter( at leat five times)

Tabulate the data and calculate along with possible errors.

Error in = R A/l so that RRAAll

How do you estimate A? Part B (graphical analysis)

Linear graph paper

Let us consider the case of time period T of a simple pendulum which is written as

T = (2) (L/g)1/2----------(1) L is the length of the pendulum while g is acceleration due to gravity. Eq. (1) can be rewritten as

T2 = (42/g) L---------(2)

Eq. (2) is an equation of straight line with slope = (42/g) and intercept = 0 One can find the value of g from the graph of T2 with L. In one of the experiments on simple pendulum a student came up with the following data

Table 1

S. No Time for 10 oscillations

(s)

Effective length of the pendulum

(m)

1 16 0.6

2 18 0.8

3 20 1.0

4 22 1,2

5 24 1,4

6 25 1.6

7 27 1.8

8 28 2.0

Find the value of g by plotting the above data i.e T2 Vs L; T is the time period of the pendulum for its effective length L.

How to plot the graph

Step 1. From Eq. 2 we have to plot T2 vs L (L should in meter)

Prepare the Table with following headings (prepare directly in your Lab Report Sheet)

Sample Table

S.No. L

(m)

T

(s)

T2

1. 0.6 1.6 2.56~2.6


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Step 2. Choose a linear graph sheet which is linearly (normally in mm) graduated on both X as well Y- axis

Step 3. Choose Y-axis for T2 and X-axis for L

Step 4. Max T2 is 1 and min is 0.25; choose your scale so that you can mark 0.25 clearly.

Similarly choose scale for L on X-axis.

Step 5. Mark the points on the graph with a sharp pencil

Step 6. Draw a straight line through the points so that maximum number of points are very

close to the line (Best fit we will not discuss presently)

Step 7. Find the slope from the graph and calculate g

Exercise

In the above experiment the error ( in time period T is (0.1s) while the length L has error

(L) equal to 0.01m. Calculate the error in g Semi-log graph paper

Radioactive decay is given by N(t) = N(0) e-at , where N(t) are the observed counts at time t,

N(0) are the counts at time t = 0 (fixed arbitrarily) and a is the decay constant. Calculate N(0)

and a by graphical technique from the given data (Table 2)

N(t) = N(0) e-at

Or ln N(t) = ln N(0) - t (ln is log to the base e)

Or 2.3log N(t) = 2.3 log N (0) -t (change of log base to 10)

Or log N(t) = log N(0) - (/2.3) t.(3)

This is an equation of a straight line with y=log N(t), x- - (/2.3) t with log N(0) as intercept

and plot of log N(t) vs t will give values of . Since y is in log form and x is in linear form the plot has to to prepared using semi-log graph paper whose y-axis is in log scale while x-axis is in linear scale.

Table 2 summarizes the data collected from an experiment on radioactive decay. Plot the data

on semi-log paper and calculate and N(0) for this decay.

Exercise: Half-life is defined as the time needed to have [N(t)/N(0)]= ; derive an expression for . Calculate the value of for the radioactive process tabulated in Table 2.

Table 2

Time (days) Relative Activity

0.2 35.0

2.2 25.0

4.0 22.1

5.0 17.9

6.0 16.8


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8.0 13.7

11.0 12.4

12.0 10.3

15.0 7.5

18.0 4.9

26.0 4.0

33.0 2.4

39.0 1.4

45.0 1.1

Important:

(i) Give a title to the graph; in present case it will be T2 Vs L for a simple pendulum.

(ii) Mark scales on the graph sheet; X-axis 10mm = so many m and Y-axis 10mm= so

many seconds (iii) Mark X-axis and Y-axis with quantity (along with units) you are plotting

(iv)Calculate the slope and g on the graph sheet so that a graph is complete and one need not to refer to the Lab Sheets.

Interpolation: From the graph you can find the L for T=0.44 (for example, within the

present data set)) even though there is no experimental data; this process is called

interpolation.

Extrapolation: One can extend the length of the line so that one can predict L for T =0.1s or

2.5s (outside the present data set); this is called extrapolation.

Cautions:

1.Zero error of the instrument must be taken in to account.

2.The cap of screw gauge should be turned till the object is just held between jaws without

pressure.

Learning outcomes: to be written by the students in 50-70 words.


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Experiment 2.

Aim: To study variation of angular acceleration with torque acting on the fly wheel. Find out

the minimum torque required to overcome the friction between the flywheel and bearing and

also find out the moment of inertia of the flywheel

Apparatus Required: A wall mounted flywheel, slotted mass with hanger (50gm each), a strong and thin string or fine cord, stop watch, meter rule or measuring tape and vernier callipers.

Learning Objectives:

Rotational dynamics Learn to Measure the angular acceleration , torque and hence moment of inertia of the flywheel.

Learn to apply the principle of conservation of energy to rotational dynamics.

Learn to aware of the limitations in an experiment and devise method to solve the problems.

Learn to handle error estimation using sum of percent errors.

Diagram and Theory:

Fig 1 Typical flywheel, slotted weights with hanger and thread

The Newtons law for linear motion that rate of change of linear momentum is equal to applied force causing the change, F= dP/dt=d(mv)/dt=ma (m=mass and a is linear

acceleration) becomes for angular motion as:

Applied torque dL/dt= d(I)/dt= I where I the rotational equivalent of mass is called

moment of inertia and is angular acceleration. Note , L and are all vectors.

Note that = r x F where F is the force applied at a distance r from the axis of rotation.

Exercise: Figure out differences between mass and moment of inertia


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Fig 2 Experimental setup

A torque to a flywheel, in this experiment, is applied by a mass M falling under gravity. This mass M is attached to one end of a thread while the other end is attached to the

axle of the flywheel. This resulting torque causes rotational motion in the flywheel. However, the friction in the bearings of the flywheel results in the frictional torque f on the bearings which oppose the motion of the flywheel.

Procedure:

Examine the wheel and see that there is the least possible friction. Measure the diameter of the axle with vernier calipers at different points and find the mean. Take a strong and thin string whose length is less than the height of the axle from the floor. Make a loop

at its one end and slip it on the pin A on the axle. Tie a suitable mass to the other end of the string.

Suspend the mass by means of the string so that the loop is just on the point of slipping from the pin A. Note the position of the lower surface of the mass m on a scale fixed behind on the wall.

Now rotate the wheel and wrap the string uniformly round the axle so that mass is slightly below the rim of the wheel. Count the number of turns wound the axle and let it is n. The wheel will thus make n revolutions before the thread detached.

With the help of stopwatch note the time taken by the mass to descend through a height h Repeat step-5 keeping m constant and varying the number of turns n. Take 6-7 readings. Again repeat step-5 keeping the number of turns n constant and varying the mass m. Take atleast 6

observations with different values of m. Repeat each observation thrice and calculate the average time

taken in each observation.

Scope of the result expected:

The student will learn about torque, angular acceleration produced due to torque and hence

physical importance of the moment of inertia of circular bodies like wheels.

Parameter and Plots: Calculate Vernier constant of vernier calliper

Calculate the radius of the axle


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To find angular acceleration: Angular acceleration of the fly wheel can be calculated by calculating the time as given in step 5 and 6. Hence draw a graph between n and t2. Slope of this graph gives us the value of angular

acceleration.

To find out torque acting on the flywheel: Suppose the mass m, when released, starts moving downward with acceleration . Let T be the tension in the string. Then the torque acting on the string can be calculated by using these parameter.

To find out moment of inertia: Plot a graph between angular acceleration along X-axis and torque along Y-axis. When we plot a graph between torque and angular acceleration, then slope of the straight line gives the moment of the inertia. Also by using the values of torque and angular acceleration, moment of

inertia can be calculated.

Sources of errors-

1--The angular velocity has been calculated on the assumption that the friction remains

constant when the angular velocity decreases to zero,but in actual practice friction increase as

velocity decreases.

2The instant at which the string is detached can not be correctly found out.

Cautions:

Mass of string can be taken into account for better results. Stop watch should be started and stopped with accuracy to avoid any kind of time interval

measurement error.



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EXPERIMENT NO. 3

Experiment: To study the dependence of force of friction on (a) Normal

reaction, (b) Area of contact, (c) Nature of material, (d) Nature of surface

APPARATUS REQUIRED: Inclined plane apparatus provided with removable glass top,

wooden blocks, scale pan, thread, spirit level and a weight box.

LEARNING OBJECTIVE: To familiarize the students with force of friction & its

dependence on normal reaction, area of contact, nature of material & nature of surface.

FORMULA USED: F R F= R, where F= force of friction =coefficient of friction R=normal reaction

PROCEDURE:

Weight the scale pan (p) & each of the wooden blocks (w).

Place the inclined plane horizontally on the table & level it with the help of a spirit level.

Make pulley fitted to inclined plane apparatus free by oiling it.

Attach one end of the thread to the scale pan & the other end to the hook of the wooden block.

Place the block on the inclined plane apparatus & pass the thread over the pulley.

Place the weight in the pan & tap the surface of the inclined plane gently. The weight should be placed in the pan in order the wooden block just begin to slide on tapping the

horizontal surface.

Note down the weight in the pan (P1); then the force of friction, F1=p+P1 & normal reaction, R1=w. Now place a known weight (W) on the wooden block & again find

weights (P2) to be placed in the pan in order that the wooden block just begin to slide on

tapping the horizontal surface. Then, then the force of friction, F2=p+P2 & normal

reaction, R2=w+W.

If F1/R1=F2/R2, then F R. Now remove the glass top of the inclined plane apparatus carefully & the place the wooden block on it & repeat the procedure as mentioned

above. Now replace the block with other identical block but having rough surface &

repeat the procedure as above.

OBSERVATIONS:

A) To study the dependence of force of friction on normal reaction:


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S.No. Weight on the

block (W)

Normal

reaction

(R=w+W)

Weight in the

pan (P)

Force of friction

(F=p+P)

F/R=

1

2

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B) To study the dependence of force of friction on area of contact:

S.No. Wooden block placed Weight in the pan (P) Force of friction (F=p+P)

1 Larger area

2 Smaller area

C) To study the dependence of force of friction on nature of material:

S.No. Wooden block placed Weight in the pan (P) Force of friction (F=p+P)

1 Glass top

2 Wooden top

D) To study the dependence of force of friction on nature of surface:

S.No. Nature of wooden block

placed

Weight in the pan

(P)

Force of friction (F=p+P)

1 Smooth surface

2 Rough surface

PLOT: Force of friction & normal reaction, a plot between F & R.

CAUTIONS:

The surface of the apparatus should be clean & dirty.

The segment of the thread between block & the pulley should be horizontal.

The pulley should be free from friction.

Tap the surface of the apparatus gently.

The scale pan should not touch any part of the table. SOURCES OF ERROR:

The dust particles on the plane surface increase the force of friction between the surfaces in contact.

The weight of the thread should be taken into account.



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EXPERIMENT NO. 4

Experiment: To plot graph between distance knife edges from the center of gravity and the

time period of a compound pendulum.

Equipment Required: Bar Pendulum, Small metal wedge, Spirit level, Telescope, Stop watch,

Meter rod, Graph paper


1. To determine the acceleration due to gravity using compound pendulum.

2. To determine the radius of gyration and the moment of inertia of the bar about an axis

passing through the centre of gravity.

Theory:

A bar pendulum is the simplest form of compound pendulum. It is in the form of a rectangular

bar (with its length much larger than the breadth and the thickness) with holes (for fixing the

knife edges) drilled along its length at equal separation. Two knife-edges are placed

symmetrically with respect to C.G as at A and B.

The time period of the compound pendulum about a horizontal axis through Centre of

Oscillation is the same as about Centre of Suspension.

Where L is the length of an Equivalent Bar pendulum

Procedure:

1. Paste a small piece of paper on either end of the compound pendulum. 2. Draw a line parallel to the edge of the pendulum on each paper to serve as a reference

mark. Mark on one side A and on the other side B. Place the knife-edges in the first

hole on either side parallel to each other and make them tight, so that the sharp edge is

pointing towards the centre of gravity.

3. Place a spirit level on the glass plates fixed on the bracket in the wall meant for suspending the pendulum and see that the upper surfaces of the glass plates are in the

same level.

4. Suspend the pendulum from the knife-edge on the side A so that the knife -edge is perpendicular to the edge of the slot and the pendulum is hanging parallel to the wall.

5. Adjust the eye-piece of the telescope so that the cross wires are clearly visible through it. Focus the telescope at the reference line of the compound pendulum.

6. Set the pendulum into vibration with small amplitude of about 50 and allow it to make a few vibrations so that these become regular.

7. Look through the telescope and when the image of the reference mark passes across the point of intersection of the cross-wires, start the stop watch and count zero. Count one when the pendulum is passing through the same position in the same direction and so

on. Note the time taken for 20 vibrations. Repeat again and take the mean.

8. Measure the distance between the C.G. and the inner edge of the knife -edge. 9. Now suspend it on the knife-edge on the side B and repeat the observations. 10. Repeat the observations with the knife-edges in the 2nd, 3rd, 4th etc. holes on either side

of the centre of gravity.

Note: See that the knife -edges are always placed symmetrically with respect to C.G.


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Observations:

S.No Side A Side B

Time for 20

vibrations

Time

Period t

(Mean/20)

Distance

from

C.G.

Time for 20

vibrations

Time

Period t

(Mean/20)

Distance

from

C.G.

1 2 Mean 1 2 Mean

1.

2.

3.

To Plot the graph:

1. Take the Y-axis in the middle of the graph paper .Represent the distance from the C.G. along

the X-axis and the time-Period along the Y- axis. 2. Plot the distance on the side A to the right and the distance on the side B to the left of the

origin.

3. Draw smooth curves on the either side of the Y-axis passing through the plotted points

taking care that the two curves are exactly symmetrical as shown in graph.

To find the value of g: 1. Draw two lines parallel to the X-axis cutting the curves at the points CAGBD and

CAGBD respectively. Also draw the line MON touching the two portions of the graph at M and N respectively.

2. Select points like C and B, A and D etc. on the graph on the two sides of the C.G., not equidistant from it, having the same time period. Measure the distance AD and CB.

3. Similarly measure the distance AD and CB. Mean L/t

2 =

Hence = ms-2

Actual value of g=9.8 ms-2A

To find the radius of gyration: Measure the distances GD, AG; GC, BG; GD, AG ; GC,BG; as well as NO and MO.

S.No. L1 L2 K=

1 GD AG

2 GC BG

3 GD AG

4 GC BG 5 NO MO

Moment of inertia:

Find the mass of the pendulum

Mass of pendulum M= kg

Radius of gyration K= m

Hence, Moment of inertia MK2= kg-m

2

Error analysis:

Percentage Error = X100

Cautions:


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1. The knife -edges should be horizontal and the bar pendulum parallel to the wall. 2. Amplitude should be small. 3. The time period should be noted after the pendulum has made a few vibrations and the

vibrations have become regular.

4. The two knife-edges should always lie symmetrically with respect to the C.G. 5. The distance should be measured from the knife-edges. 6. The graph drawn should be a free hand curve.



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EXPERIMENT NO. 5

Experiment: To determine the value of acceleration due to gravity at a place by

Kater's pendulum.

Apparatus used: Katers Pendulum, Telescope, Stop watch, Meter scale, Sharp wedge, rigid support.

Learning Objectives

1. To determine the acceleration due to gravity (g) using Katers pendulum. 2. To verify that there are two pivot points on either side of the centre of gravity

(C.G.) about which the time period is the same.

Formula used:

Theory

Katers pendulum is a Compound pendulum based on the principle that the centre of suspension and centre of oscillation are interchangeable. The movable

cylinders, knife edges and the metallic weight are so adjusted such that the time

periods of the pendulum about the two knife edges situated asymmetrically with

respect to the center of gravity are exactly equal. Then, the distance between the

knife edges is equal to the length of equivalent simple pendulum whose time

period is given by

And from here we can calculate the value of g as

Hence, g may be calculated.

We resort to Bessels approximation where we require making the two time periods to be nearly equal because it is quite difficult and time-consuming to set

the Katers pendulum so that the time period becomes exactly equal about two points.

If T1 and T2 represent two nearly equal time periods (in sec) for positions

of K1 and K2 distant l1 and l2 (in cm) from C.G., then we can write


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Since T1~T2 and positions of K1 and K2 are asymmetrical about C.G, l1-l2 is fairly

large. Hence, the second term in the denominator is negligibly small and thus, an

approximate value of l1-l2 is sufficient.

Therefore,

(1)

Where

g = Acceleration due to gravity in cm/s2

T1 = Time period about K1 in seconds

T2 = Time period about K2 in seconds

l1 = Distance of K1 from C.G. in cm

l2 = Distance of K2 from C.G. in cm

Procedure:

1. Determine the middle point of the rod and fix the smaller metal weight W there. Fix the brass weight W1 near one end of the Katers pendulum and the knife edge K1 just below it.

2. Similarly, adjust the wooden weight W2 and the knife edge K2 at the other end (end 2) of the pendulum with the same symmetry. The metallic and wooden

cylinders are placed at different ends to eliminate viscous drag of air and to

make the C.G. asymmetrical about the knife edges .Screw all the five tightly.

Knife edges must be sharp, horizontal and parallel to each other so that the

oscillations are confined to a vertical plane.


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3. Suspend the pendulum vertically about K1 and focus the telescope at the tip of its lower end. Set it oscillating with amplitude of about 4-5 degrees for the

motion to remain simple harmonic. Note the time for 30 oscillations using a

stop watch.

4. Now suspend the pendulum vertically about K2 and repeat step 3.This time will be quite different from that about K1.

5. Keep moving K1 and K2 towards W by small distance (approx. 1 cm) and repeat steps 3 and 4 till the difference in time about K1 and K2 is less than one

second. If at any stage the time difference increases, then K1 and K2 should be

moved towards W.

6. Now, move the weight W and repeat step 5 to reduce the time difference to about 0.5 second.

7. The apparatus is ready to record the measurements. Suspend the pendulum about K1 and K2 vertically and record the time taken for 100 oscillations.

Repeat this 5 times each.

8. Remove the pendulum from support and place it horizontally on a wedge. Balance it and find the C.G. of the system.

9. Measure the distances of knife edge K1 and K2 from the center of gravity.

Observations

Least count of meter scale = ------ mm

Least count of stop watch = ------ sec.

Knife edge Time for 100 vibrations Time

period 1 2 3 mean

K1 T1=

K2 T2=

Calculations

T1 = ------ sec

T2 = ------ sec

l1 = ------ cm

l2 = ------ cm

Substitute in the Equation (1) and obtain the value of g.

Result

The value of acceleration due to gravity g as calculated in the lab is (---------

max. log error) cm/s2.

Percentage error

The percentage error can be calculated as

Standard value calculated value


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Percentage error = ---------------------------------------------- X 100

Standard value

Where

Standard value = 9.81 cm/s2

Calculated value = g

cautions:

1. The heavy weight should be placed at one end so that the C.G. lies near one

end of the Knife edges and wooden weight symmetrically at the other end to

avoid the error due to air drag.

2. The amplitude of vibration should be small so that the motion of the pendulum

satisfies the condition sin = . 3. For final observations the time period must be taken with an accurate stop

watch.



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EXPERIMENT NO. 6

Experiment: To find the moment of inertia of an irregular body about an axis through the

centre of gravity with a torsion pendulum.

Equipment Required: Moment of inertia table, a regular body (right circular cylinder or

cube), an irregular body, spirit level, vernier calipers, telescope with an inverted scale with a zero mark in middle, a stop watch, a balance and a weight box.


1. To familiarize students with the concept of moment of inertia.

2. To familiarize students with the concept of torsion and modulus of rigidity.

Outline of the Procedure:

1. Suspend the moment of inertia table by means of a copper wire of a suitable length and thickness from a rigid support. Place a spirit level amongst the diameter and see that the

table is horizontal. If it is not horizontal, then adjust the nuts provided at the ends of the

two rods.

2. Place a telescope with an inverted centimeter scale clamped to its stand at a distance not less than one meter towards the mirror fixed to the torsion head.

3. Place the eye just above the telescope and adjust the position of the scale so that the images of the scale divisions are seen in the mirror. Now place the telescope in the position of the eye.

4. Adjust the eye piece of the telescope so that the cross-wires are clearly visible.

5. Twist the table 5-6 times so that it begins to execute torsional vibrations. Count time for 5 vibrations. Repeat three times.

6. Now, place the regular body in the centre of the table. Adjust the position of the table to check if it is perfectly horizontal. Repeat step 5.

7. Remove the cylinder and place the irregular body on the table. Adjust the table so that it is perfectly horizontal. Repeat step 5.

8. Weigh the regular body and find its dimensions with the help of vernier calipers.

Observations:

Sr. no. Time for 5 vibrations Time period

(mean/5)

1 2 3 mean

1 Table alone t

2 With regular

body

t1

3 With irregular

body

t2


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Mass of the regular body: kg

Dimensions of the regular body

1. For cylinder:

Diameter of the solid cylinder: 1.

2.

3.

Mean diameter, d=. cm

Mean radius, r = . cm =.. m

2. For cube:

Edge length: 1.

2.

3.

Mean edge length, a = .cm = . m

Moment of inertia of regular body (

1) For cylinder

2) For cube:

Calculations:

Moment of inertia of irregular body; =

= kg-m2

Result: The moment of inertia of the irregular body is . kg-m2

Error analysis--NA

cautions:

The moment of inertia table should be always horizontal. The moment of inertia table should execute torsional vibrations only.

The amplitude should be small so that the wire is not twisted beyond the elastic limits.



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EXPERIMENT NO. 7

Experiment : To determine the frequency of a electrically maintained tuning fork by using

Meldes experiment and hence verify the law of vibrating string.

Equipment Required: Electrically maintained tuning fork, Clamp stand, pan, weight box,

rheostat, key, connecting wire, meter rod.

Material Required: Thread

Learning Objectives: To understand the formation of standing waves in transverse and longitudinal waves and also study laws of string.


1.A string can be set into vibrations by means of an electrically maintained tuning fork,

thereby producing stationary waves due to reflection of waves at thepulley. The standing wave is formed between the pulley and the end of the string


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2.Find the weight of pan P and arrange the apparatus as shown in figure. Place a load of 4 To 5

gm in the pan attached to the end of the string passing over the pulley. Excite the tuning fork

by switching on the power supply. Adjust the position of the pulley so that the string is set into

resonant vibrations and well defined loops are obtained. If necessary, adjust the tensions by

adding weights in the pan slowly and gradually. For finer adjustment, add milligram weight so that nodes are reduced to points.

3. Measure the length of n loops formed in the middle part of the string. If L is the distance in which n loops are formed, then distance between two consecutive nodes is L/n. Note down the weight placed in the pan and calculate the tension T. T= (wt. in the pan + wt. of pan) g 4--Repeat the experiment twine by changing the weight in the pan in steps of one gram and altering the position of the pulley each time to get well defined loops. 3)

Measure one meter length of the thread and find its mass to find the value of m, the mass

per unit length.

OBSERVATIONS:

Mass of the pan, W = kg


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Mass per meter of thread, m = --kg

For transverse arrangement,

Mean frequency, n= vib/sec

For longitudinal arrangement,

Mean frequency, n= vib/sec

Required Results: Find the frequency of tuning fork in transverse mode and also in longitudinal

mode. Observe and discuss the difference between these arrangements.

Graphs/Plots: Also show and plot {(2)/T} = constant

These variations can also be plotted.

For studying laws of string discuss the observations according to i) law of mass ii) law of length

iii) law of tension iv) law of diameter and v)law of density.

ERROR ANALYSIS;Find various sources of erreos and do calculate percentage error..

Cautions:

1.The thread should be uniform and inextensible.

2 Well defined loops should be obtained by adjusting the tension with milligram weights.

3 The loops in the central part of the thread should be counted for measurement. The nodes at the tip of the prong and at the pulley should be neglected.

4 Frictions in the pulley should be least possible.



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EXPERIMENT NO. 8:

EXperimnt: To study one dimensional elastic collision using two hanging sphere.

Equipments to be used: two metallic spheres of equal masses, a metre rod,

light & uniform thread, fixed unyielding support with suspension head to

suspend the spheres.

Learning Objectives: To learn to study the one dimensional elastic collision To learn to apply the principle of conservation of energy & momentum To understand the limitations of the experiment set-up and devise

a method to overcome those limitations. Procedure:

Find the weight of the two metallic spheres P & Q separately. See that the two are nearly equal as possible.

Suspend the two spheres with threads of the same length L from the suspension clamps & see that they are perfectly vertical.

Place a meter scale horizontally below the spheres. Note the initial positions of the spheres on the meter scale when at rest.

Now displace the sphere P towards the left through a distance of 4 to 5cmto the position P & then release it. The sphere P will strike against the sphere Q. As their masses are equal, the sphere P will come to rest after

collision (which is elastic for all purposes) while, the sphere Q would move towards the right Note the position Q upto which the sphere Q moves to the right before retracing its path. If the two spheres are of exactly the same

mass, then the sphere q will travel through exactly the same distance as

travelled by the sphere P from the point of release to the position of sphere Q while at rest. Repeat the experiment 6 to 7 times to get the exact distance travelled by the sphere P & Q before & after collision.

Scope of results to be reported: Mass of sphere P, m1 = ---------------- gm

Mass of sphere Q, m2 = ---------------- gm

Distance between spheres P & Q, when at rest, y = ------- cm

Law of Conservation of linear momentum:


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Since velocity is proportional to horizontal distance

Initial velocity of P before collision, u1 = ks1 Final velocity of P after collision v1 = 0

Initial velocity of Q before collision, u2= 0

Final velocity of Q after collision v2= k s2 According to Law of Conservation of linear momentum

m1 u1 + m2 u2= m1 v1 + m2 v2

m1 ks1 + m2 x 0= m1 x0 + m2 k s2

m1s1 = m2s2 -------- = ---------

By actual calculations it is found to be correct (with in experimental error)

Law Conservation of Kinetic energy: 1/2m1u21 + 1/2m2u22= 1/2m1v21 +1/2 m2v22

1/2m1k2s21 =1/2m2k2s22

m1s21 = m2s22 ------- = ---------

Parameters and plots:

From calculations, law of conservation could be found correct (with in experimental error) ERROR ANALYSIS;Find various sources of errors.

Cautions:

1. The collision should be one dimensional & elastic.

2. The ball P should strike the ball Q in a manner so as to have a head on

collision.

3. The masses of the two spheres should be exactly equal.

4. The amplitude of sphere P should be small, so that the velocity is

proportional to displacement.



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EXPERIMENT NO. 9:

Experriment : To determine the Youngs modulus of the material of a rectangular bar by beam bending using Travelling microscope.

Apparatus required : A beam of rectangular cross section (meter scale), two knife-edge

supports, a stirrup with a hook ,a hook to carry the load, slotted weights, spherometer, vernier

calipers and screw gauge, Travelling microscope.

Learning objectives :

To learn to find the Youngs modulus of the material.

To understand the limitations of the experiment set-up and devise a method to overcome

those limitations.

Theory :

Consider a bar supported on two knife edges in a horizontal plane so that equal lengths of the bar

project beyond the knife edges. If a weight mg is suspended at the middle point, a depression y is

produced.

For a rectangular bar of breadth b and thickness d the depression, Youngs modulus Y is

Y = (mgl3 ) / (4ybd3 )

Diagram :


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Image of speherometer

Procedure :

Find the center of gravity of the given bar and draw a sharp transverse line at the position

of C.G.

Place the bar on the two knife edges as shown in figure so that it rests on the two marked

lines equidistant from C.G. Make the bar horizontal and test with a spirit level.

Slip the stirrup on the bar and adjust its position so that the tip of the needle lies vertically

above the line marked at C.G. Suspend the hanger from the hook.

Find least count of spherometer and note its reading for no load on the hook.

Slip a half kg weight on the hanger gently. Work the micrometer screw and again note the

reading on spherometer.

Gradually increase the load in steps of half kg and take such eight observations.

Now decrease the load in steps of half kg and take the readings as before.

Remove the bar carefully without disturbing the position of knife edges. Measure the

distance between the two knife edges accurately using meter-scale.

Measure the breadth of the bar with a vernier callipers and thickness with a screw gauge at

5 points.

Plot a graph between the load and the mean of corresponding microscope readings on

loading and unloading. Find from the graph mean depression for two kg.

Observations : Least count of the spherometer = .. mm Observation table :

Mean depression for 2 kg by calculations from graph

y = .. mm = m Length of the bar between two knife edges Mean l = .. m

Using vernier calipers : least count = 0.01 cm

Breadth of the bar Mean b = . m


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Using screw gauge: least count = 0.01 mm

Thickness of the bar Mean d = mm = .. m. Substitute the values in the expression :

Y = (mgl3 ) / (4ybd3 ) = . N/m2

ERROR ANALYSIS;Find various sources of errors and Find the corresponding percentage

error (if any).

cautions:

The Knife-edges should be rigid & fixed on a rigid support

The Knife-edges should be at equal distances from the centre of the bar. The stirrup

should be parallel to the Knife-edges & placed exactly at the centre to get a

symmetrical loading of the bar.

The weights should be placed or removed from the hanger gently & should be

increased or decreased gradually in equal steps.

The maximum load used should be such that it keeps the bar within elastic limits.

The thickness should be measured very accurately at a number of points along the

whole length of the bar. The thickness d is a small quantity & since its cube is to be

used in the calculations, a small error in its measurement will cause three times large

error in the result.



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EXPERIMENT NO. 10

Experiment: To Study the induced e.m.f. as function velocity of the magnet.

Equipment Required: A small permanent magnet mounted at the middle of a semi-circular arc, a

coil consisting of number of turns, two weights, stopwatch, capacitor, diode, resistance, voltmeter

Material Required: A small strong permanent magnet, a stopwatch


Electromagnetic induction

Induced e.m.f

Dependence of the magnitude of induced e.m.f on the velocity of the magnet.


Mount the magnet at the middle point of the semi-circular arc and suspend the rigid

aluminium frame from its centre so that whole frame can oscillate freely through the coil.

Adjust the position of two weights on the diameter arm of the arc to have minimum time

period.

Connect the terminals of the coil to the diode circuit for measuring the peak value of

induced e.m.f.

Note time for about 20 oscillations with an amplitude of about say 20cm and respective

peak voltage.

Repeat thrice keeping the amplitude same and find the time period. Also note the peak

voltage each time.

Repeat the experiment after changing the amplitude and take 8-10 readings.

Now change the time period by adjusting the position of the weights on the diameter arm.

Take about three readings at this position.

Repeat the experiment after changing the time-period and take 8-10 readings.

Scope of the results expected: This experiment will help in understanding the nature and polarity

of induced e.m.f. One can apply the acquired knowledge to see the dependence of induced e.m.f. on

velocity of magnet w.r.t. the pickup coil.

Parameters and Plots:

(A) Time period constant, amplitude variable:

Mean position of the centre of the magnet= cm.


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Radius of the semi-circular arc R0= cm.

Sr.No. Amplitude

a = R00

Time for 20

Oscillations

Mean time

period(T)

eo eo/a= eo/ R00 Linear velocity

v = (2/T) R00

1

.

.

.

(i)

(ii)

(iii)

Mean

2

(B) Amplitude constant, time period variable:

Sr.No. Amplitude

a = R00

Time for 20

Oscillations

Mean time

period(T)

eo eoT Linear velocity

v = (2/T) R00

1

(i)

(ii)

(iii)

Mean

Model Plot:


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ERROR ANALYSIS;Find various sources of errors .

Cautions:

The semi circular frame should oscillate freely as a whole on the knife edge.

The magnet should pass freely through the coils.

The magnet should be small and should be mounted at the middle of the semi circular arc.



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EXPERIMENT NO. 11:

Aim: To determine the modulus of rigidity of copper wire by Maxwels needle. Equipments to be Used: A Maxwells needle, a copper wire of suitable length & thickness, a fixed support with tension head, a telescope with a scale attached to its stand , stop watch, a

screw gauge, a spring balance, a meter rod & an electric lamp with holder.


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Error analysis-Calculate percentage error and find various sources of errors.


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PHY121

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