CONTENTS

1. Vernier Calipers 1

2. Screw Gauge 4

3. Simple Pendulum 7

4. Moment Bar 9

5. Convex Lens 12

Appendix 15

1

Vernier Calipers

Exp. No: 1Date:

Aim

(i) To �nd the volume of the given cylinder by measuring its length and diameter

(ii) To �nd the volume of the given rectangular block by measuring its length, breadth and thickness

Apparatus

Vernier caliper, metallic cylinder and rectangular block

Principle

Vernier caliper consists of a metal scale graduated in mm which forms the main scale. It has a �xedjaw J1 at one end and a movable jaw J2 provided with a vernier scale which slides over the mainscale. The least count of the vernier is the smallest distance that can be measured with it and it canbe calculated using the equation,

Least count of vernier (LC) =Value of one main scale division (MSD)

Number of divisions on the vernier scale(1)

Total reading =MSR + (V SR× LC) (2)

where MSR is the main scale reading and VSR is the vernier scale reading.

If l is the length of the cylinder and r is the radius of the cylinder,

Volume of the cylinder, V = πr2l (3)

If l is the length, b is the breadth and t is the thickness of the rectangular block,

Volume of the rectangular block, V = lbt (4)

Procedure

The value of one main scale division and number of divisions on the vernier scale are noted. Theleast count of the vernier is calculated using equation (1).

To �nd the volume of the cylinder

The given cylinder is gently gripped lengthwise between the jaws of the vernier caliper. The mainscale reading (MSR) just before the zero of the vernier scale is noted. The vernier scale reading(VSR) coinciding with some division on the main scale is also noted. The length of the cylinder isthen calculated using equation (2). The experiment is repeated �ve times and the average value ofthe length of the cylinder is calculated.

1

The cylinder is gently gripped diameter-wise between the jaws. Main scale reading and vernierscale reading are noted and the diameter of the cylinder is then calculated using equation (2). Theexperiment is repeated �ve times and the average value of the diameter of the cylinder is calculated.The half of the mean diameter gives the radius of the cylinder. The volume of the cylinder is thencalculated using equation (3).

To �nd the volume of the rectangular block

The given rectangular is gently gripped lengthwise between the jaws of the vernier caliper. The mainscale reading (MSR) just before the zero of the vernier scale is noted. The vernier scale reading(VSR)coinciding with some division on the main scale is also noted. The length of the rectangularblock is then calculated using equation (2). The experiment is repeated �ve times and the averagevalue of the length of the rectangular block is calculated. The same procedure is repeated to �ndthe breadth and thickness of the rectangular block. The volume of the rectangular block is thencalculated using equation (4).

Result

Volume of the given cylinder = m3

Volume of the given rectangular block = m3

Observations and Calculations

Value of one main scale division = cm

Total number of divisions on the vernier scale =

Least count of vernier (LC) =Value of one main scale division (MSD)

Number of divisions on the vernier scale

=

= cm

(i) To �nd the volume of the cylinder

DimensionTrialNo

MSR (cm) VSRTotal Reading =

MSR + (VSR x LC)(cm)

Mean (cm)

Length of thecylinder

12345

Diameter ofthe cylinder

12345

2

Length of the cylinder (l) = cm

Diameter of the cylinder (D) = cm

Radius of the cylinder (r) =D

2

=

= cm

Volume of the cylinder = πr2l

=

= cm3

= ×10−6 m3

(i) To �nd the volume of the rectangular block

DimensionTrialNo

MSR (cm) VSRTotal Reading =

MSR + (VSR x LC)(cm)

Mean (cm)

Length of therectangularblock

12345

Breadth oftherectangularblock

12345

Thickness oftherectangularblock

12345

Length of the rectangular block (l) = cm

Breadth of the rectangular block (b) = cm

Thickness of the rectangular block (t) = cm

Volume of the rectangular block (V) = lbt

=

= cm3

= ×10−6 m3

3

Screw Gauge

Exp. No: 2Date:

Aim

(i) To �nd the volume of the given wire by measuring its length and diameter

(ii) To �nd the volume of the given glass plate by measuring its thickness and area

Apparatus

Screw Gauge, metal wire and glass plate

Principle

Screw gauge works on the simple principle of converting small distances into larger ones by measuringthe rotation of the screw. When the head of the screw gauge is rotated, the distance moved by thescrew for every complete rotation is a constant called pitch of the screw.

Pitch of the screw gauge (P) =Distance moved

Number of rotations(1)

Least count of the screw gauge (LC) =Pitch (P)

Number of divisions on the head scale (N)(2)

Total reading = PSR + (Corrected HSR× LC) (3)

where PSR is the pitch scale reading and HSR is the head scale reading.

If l is the length of the wire and r is the radius of the wire,

Volume of the wire, V = πr2l (4)

If t is the thickness and A is the area of the glass plate,

Volume of the glass plate, V = At (5)

Procedure

The pitch, least count and zero error of the screw gauge are determined �rst. The head of the screwgauge is given six complete rotations and distance moved by head over the pitch scale is noted. Thepitch of the screw gauge is calculated using equation (1). The number of divisions on the head scaleis noted and least count of the screw gauge is calculated using equation (2).

To �nd the zero error, the screw head is rotated until the two plane faces are just in contact. Ifthe zero of the head scale coincides with the reference line on the pitch scale, the instrument has nozero error and hence, no zero correction. If the zero of the head scale is above the reference line (sayby 5 divisions), the zero error is -5 div and zero correction is +5 div. If the zero of the head scale isbelow the reference line (say by 5 divisions), the zero error is +5 div and zero correction is -5 div.

4

This correction is to be added to the observed head scale reading (HSR) when the measurement istaken.

To �nd the volume of the wire

The diameter of the wire is measured by gently gripping the wire between the plane faces of thescrew gauge. Pitch scale reading (PSR)just before the head of the screw gauge is noted. Head scalereading (HSR) coinciding with the reference line on the pitch scale is also noted. The diameter ofthe wire is then calculated using equation (3). The experiment is repeated �ve times and the averagevalue of the diameter of the wire is calculated. The half of the mean diameter gives the radius ofthe wire. The length of the wire is measured using a meter scale. The volume of the wire is thencalculated using equation (4).

To �nd the volume of the glass plate

The given glass plate is gently gripped between the plane faces of the screw gauge. The pitch scalereading and head scale reading are noted. The thickness of the glass plate is then calculated usingequation (3). The experiment is repeated �ve times and the average value of the thickness of theglass plate is calculated. To �nd the area of the glass plate, its outline is taken on a graph paperand the number of millimeter squares enclosed in it is counted. The volume of the glass plate is thencalculated using equation (5).

Result

Volume of the given wire = m3

Volume of the given glass plate = m3

Observations and Calculations

Value of one pitch scale division = mm

Distance moved for 6 rotations of the head = mm

Pitch of the screw gauge (P) =Distance moved

Number of rotations

=

= mm

Total number of divisions on the head scale (N) =

Least count of screw gauge (LC) =P

N

=

= mm

5

DimensionTrialNo

PSR (mm) HSRCorrectedHSR

Total Reading = PSR+ (Corrected HSR x

LC) (mm)

Mean(mm)

Diameter ofthe wire

12345

Thickness ofthe glassplate

12345

(i) To �nd the volume of the wire

Length of the wire (l) = mm

Diameter of the wire (D) = mm

Radius of the wire (r) =D

2

=

= mm

Volume of the wire = πr2l

=

= mm3

= ×10−9 m3

(ii) To �nd the volume of the glass plate

Area of the glass plate (A) = mm2

Thickness of the glass plate (t) = mm

Volume of the glass plate (V) = At

=

= mm3

= ×10−9 m3

6

Simple Pendulum

Exp. No: 3Date:

Aim

(i) To determine the acceleration due to gravity (g) at the place

(ii) To determine the length of the seconds pendulum from (l, T 2) graph

Apparatus

Simple pendulum, stop clock and meter scale

Principle

The simple pendulum consists of a small metallic bob suspended by a light string. The length of thependulum (l) is the distance between the centre of the bob and the point of suspension. The period(T) of the pendulum is the time taken to complete one oscillation. The relation between length ofthe pendulum, its period and acceleration due to gravity is given by

T = 2π

√l

g

T 2 = 4π2

(l

g

)

g = 4π2

(l

T 2

)(1)

Procedure

The radius of the bob is measured using vernier calipers. The length of the pendulum is equal to thedistance from the point of suspension to the top of the bob plus the radius of the bob. The lengthis initially adjusted to be 0.5 m. The time (t) for 20 oscillations is determined twice using a stopclock and mean value of t is calculated. The period T is calculated as T = t

20. The value of l

T 2 isdetermined. The experiment is repeated for l = 0.6 m, 0.7 m, 0.8 m, 0.9 m, 1 m and 1.1 m. Themean value of l

T 2 is calculated. The acceleration due to gravity (g) is calculated using equation (1).

(l, T 2) graph

A graph is plotted with l along X-axis and T 2 along Y-axis. This graph is called (l, T 2) graph. It canbe seen that (l, T 2) graph is a straight line and can be used to calculated the length corresponding toany period. For a seconds pendulum, T = 2 seconds and hence, T 2 = 4. The length correspondingto T 2 = 4 gives the length of the seconds pendulum.

7

Result

Acceleration due to gravity at the place = m/s2

Length of the seconds pendulum = m

Observations and Calculations

Radius of the bob (r) = cm

TrialNo

Legth of thependulum (l) m

Time for 20 oscillations T(s)

T 2

(s2)l/T 2

(m/s2)1 (s) 2 (s) Mean (s)1 0.52 0.63 0.74 0.85 0.9

Mean value of (L/T 2) = m/s2

Acceleration due to gravity g = 4π2

(l

T 2

)

=

= m/s2

From (l, T 2) graph, length of the seconds pendulum = m

8

Moment Bar

Exp. No: 4Date:

Aim

(i) To �nd the mass of the moment bar

(ii) To �nd the mass of the given body

Apparatus

Moment bar, weight hanger, slotted weights and unknown mass

Principle

Moment bar is a uniform bar like a meter scale. When the moment bar is in equilibrium under theaction of coplanar parallel forces, then according to principle of moments, the sum of anticlockwisemoments about any point equal to the sum of clockwise moments about the same point. The momentof a force about a given point is the product of the force and the perpendicular distance between thepoint and the line of action of the force.

Procedure

The centre of gravity (G) of the moment bar is determined �rst. The moment bar will remainhorizontal when supported at the centre of gravity. The position of G is noted by balancing themoment bar properly.

To �nd the mass of the moment bar

The moment bar is suspended at a point O on one side of the centre of gravity G as shown in Fig.1.The weight of the moment bar acts vertically downwards through the point G. A known weight Wis suspended from a point A on the bar and the position of W is adjusted until the moment barremains horizontal. Then according to the principle of moments,

M ×GO = W ×OA

M = W × OA

GO

Here M is the mass of the moment bar. The experiment is repeated by changing the value of W andthe average value of M is calculated.

To �nd the mass of the given body

The moment bar is suspended at the centre of gravity G and the given body is suspended from apoint B on one side of G as shown in Fig.2. A known weight W is suspended on the other side of Gand the position of W is adjusted until the moment bar remains horizontal. Then according to theprinciple of moments,

m×BG = W × AG

9

m = W × AG

BG

Here m is the mass of the given body. The experiment is repeated by changing the value of W andthe average value of m is calculated.

Result

Mass of the moment bar = kg

Mass of the given body = kg

Observations and Calculations

Position of the centre of gravity of the moment bar (G) = cm

(i) To �nd the mass of the moment bar

Trial NoKnown mass W

(gm)DistanceGO (cm)

DistanceOA (cm)

M = W × OAGO

(gm)

1 50 102 100 103 150 104 200 105 250 10

Mass of the moment bar = gm = ×10−3 kg

10

(ii) To �nd the mass of the given body

Trial NoKnown mass W

(gm)DistanceBG (cm)

DistanceAG (cm)

M = W × AGBG

(gm)

1 50 102 100 103 150 104 200 105 250 10

Mass of the given body = gm = ×10−3 kg

11

Convex Lens

Exp. No: 5Date:

Aim

(i) To determine the focal length of the given convex lens by distant object method

(ii) To determine the focal length of the given convex lens by u-v method

(iii) To determine the focal length of the given convex lens from (u, v) graph

Apparatus

Convex lens, stand for mounting the lens, illuminated wire gauze, white screen and meter scale

Principle

A convex lens is an optical device which converges a parallel beam of light to a point by means ofrefraction. The point at which the light beam is converged is called the focus of the convex lens.The distance between the focus and optic centre of the convex lens is called its focal length (f). Thedistance between the lens and the object is called object distance (u) and the distance between thelens and the image is called image distance (v). The focal length of the convex lens is related toobject distance and image distance by the equation,

1

u+

1

v=

1

f

f =uv

(u+ v)

Procedure

Distant object method

The approximate focal length of the given convex lens is determined �rst by distant object method.For this, the convex lens is mounted vertically on a stand and is placed in such a way as to face avery distant object. The screen is placed on the other side of the lens and its position is adjustedto get a well de�ned sharp image of the object. The distance between the lens and the screen ismeasured using a meter scale. This distance gives the approximate focal length of the lens since theimage of a distant object will formed close to the focus of the lens. The experiment is repeated 3times and the mean value of the focal length is calculated.

u-v method

The given convex lens mounted vertically on a stand is directed towards the illuminated wire gauzewhich acts as the object (Fig.1). The lens is initially placed at a distance slightly greater than theapproximate focal length obtained by distant object method. The position of the screen is adjustedto get a clear image on it. The distance between the lens and the image is measured using a meterscale. The focal length of the convex lens is calculated using the formula,

12

f =uv

(u+ v)

The experiment is repeated for both magni�ed and diminished images. The average value of thefocal length is then calculated.

(u, v) graph

A graph is plotted with u along X-axis and and v along Y-axis using the same scale factor for bothu and v. The bisector of the angle XOY is drawn to meet the (u, v) graph at a point C as shown inFig.2. From the point C on the graph, perpendiculars CA and CB are drawn to the axes. Then,

OA = OB = 2f

Hence, f =(OA+OB)

4

Result

(i) Focal length of the given convex lens by distant object method = cm

(ii) Focal length of the given convex lens by u-v method = cm

(iii) Focal length of the given convex lens from (u, v) graph = cm

Observations and Calculations

Distant object method

Distance between thelens and image of thedistant object

1 (cm) 2 (cm) 3 (cm) Mean (cm)

u-v method

Trial No u (cm) v (cm) f = uv(u+v)

(cm) Mean f (cm)

12345

13

From (u, v) graph

Distance OA = cm

Distance OB = cm

Focal length, f =(OA+OB)

4

=

= cm

14

Appendix

1. Vernier calipers

2. Screw Gauge

3. Simple pendulum

15