7/30/2019 units & measurements :Physics @ viresh

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Mechanics for CBSE -PMT, AIEEE, JEE{Dimensions, Error and measurement}

Q1 The number of fundamental quantities are(a) 5 (b) 3 (c) 7 (d) 9

Q2- Mark true / false against following statements:(i) Radian is secondary unit.

(ii) Universal gas constant R is dimensionless.

(iii) Surface tension has same dimensions as spring constant.

(iv) Plank constants unit is joule- second.Q3- Dimensional formula of the torque is(a) M L

2T-1 (b) M L

2T-2

(c) M L T-1 (d) M0

L T-1

Q4-Dimensional formula of the angular momentum is

(a) M L T-1 (b) M L2

T-2

(c) M L1

T0 (d) none of these

Q5 The plank constant has same dimensions as thedimensions of

(a) torque (b) angular momentum(c) power (d) energy

Q6- The force on a sphere of radius R moving in a mediumwith velocity v , is given by F = 6 R v. The dimensions of

the viscosity are

(a) ML3 (b) MLT-2 (c) M L2T-3 (d) M L-1

T-1

Q7- Dimensional formula of electromotive force is same asthat for

(a) force (b) energy (c) power (d) potential

Q8-The dimensional formula for the action will be(a) M L T-2 (b) M L

2T-2

(c) M L2

T-1

(d)M

2L T-2

Q9- The dimensional formula for latent heat is .Q10- Electric potential multiplied by the current is electricpower. The dimensional formula for electric potential will be

(a) M L2

T-3

A (b) M L2

T-3

A-1

(c) M L-1

T-3

A (d) M L T-2

A

Q11- When a wave propagates along x direction , then attime t , medium particles located at position x are displaced

from their mean position by A sin( t k x). Then the

dimensional formula of

(i) A is

(ii) is

(iii) k is .

Q12- Dimensional formula for impulse is ..Q13- Dimensions of electric resistance are(a) M L

2T-3

A-1 (b) M L

2T-3

A-2

(c) M L2T

-2A

-1 (d) none of these

Q14- Moment of inertia I of a sphere of mass m and radius Ris 2M R2 / 5 . If Iab has same dimensions as that for

energy, then a = --------------- and b =------------------.

Q15- Time period of a spring mass system is proportional toma Kb where m is mass of the system and K is the spring

constant. Then

(a) a = 1 ; b = (b) a = 1 /2 ; b = -1/2

(c) a = b= (d) a = 2b = -1

Q16- According to the Stefans Law of thermal radiation , ablack body at temperature T Kelvin, radiates energy E per

unit time per unit area such that E = T4, where is called

Stefans constant. The dimensions of are

(a) M L0

T-3

K-4

(b) M L2

T-3

K-4

(c) M L0

T-3

K4 (d) none of these

Q17- Dimensional formula for universal gas constant R is(a) ML3 T-2 K-2 mol-1 (b) ML2 T-3 K-2 mol-1

(c) ML2 T-2 K-1 mol-1 (d) ML2 T-2 K-1

Q18- Bulk modulus of a material has same dimension as thatof pressure. Sound wave velocity in a solid , liquid or gas isfunction of bulk modulus B and density of the medium.

If the sound wave velocity = Bab then

(i) a =-

(ii) b=

Q19- In a Vander wall gas equation ( P+ a /V2 ) ( V-b) = R T, thedimensions of a are(a) M L3 T-2 (b) M L2 T-2

(c) M L3 T-1 (d) M L5 T-2

Q20 With usual notation, following equation , said to givethe distance covered in the nth second i.e. Sn = u + a(2n-1)/2

is

(a) numerically correct only

(b) dimensionally correct only(c) both dimensionally and numerically correct

(d) neither dimensionally nor numerically correct.

Q21-In a new unit system say ABC, unit of mass is 4 kg andunit of length is 0.5 meters and unit of time is 2 second. Then

in unit system ABC one unit of force will be equal to

(a) 5 newton (b) 1 newton (c) 2 newton (d) 0.5 newton.

Q22- In unit system ABC as described in previous problem,one unit of power equals to

(a) 10 Watt (b) 8 watt (c) 20 Watt (d) 1 /8 watt

Q23- The capacitance C of a capacitor equals ratio of thecharge on the capacitor to the potential of the capacitor.

Product of the resistance and the capacitance i.e. RC willhave same unit as that of

(a) time (b) length (c) mass (d) velocity

Q24- If the energy stored in a capacitor is equal to 0.5 Cx Vywhere V is the potential of the capacitor, then

(i) x = ..

(ii) y =.

7/30/2019 units & measurements :Physics @ viresh

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Q25- Dimensional formula for viscosity is M L-1 T-1 .If a pipe of length L , diameter D carries a viscous liquid

of viscosity at pressure difference P between theends of the pipe, and volume of the liquid flowing per

unit time is Q, then if P = c x DyQz L where c is adimensionless quantity , the values of x , y and z are

.., and respectively.

Q26- Power of a machine is 120 watt. In a new unit

system 25 kg, 2 meter and 5 second are fundamental

units, then what the power the machine in new unit

system?

(a) 150 unit (b) 25 unit

(c) 1/150 unit (d) 1/25 unit

Q27-Escape velocity from a planet of density , radiusR depends on G, and R as following;

v = k Gab Rc where k is a dimensionless constant.Then with the help of dimensional analysis it can be

concluded that

(i) a =(ii) b =..

(iii) c = .

Q30- On the basis of the previous problem , find the

percentage increase in the escape velocity if the planet

expands to increase its volume by 3 % .

(a) 1% (b) -1 % (c) 0.5% (d) -0.5%.

Q31- Random errors can be minimised by

(a) changing the instrument

(b) changing the observer

(c) increasing the number of observation

Q32- Systematic error are does not include

(a) instrumental error

(b) biased personal error

(c) unbiased personal error

(d) faulty calibration of the instrument.

Q33- Mark true / false against following statements:(i) Increasing the number of observations does not

minimize the systematic error.

(ii) changing the biased observer may reduce the

systematic error.

(iii) Absolute error can never be negative.

Q34- Area of a square is given as (100 2 ) cm2 .The side of the square is

(a) (10 2 ) cm (b) (10 1 ) cm

(c) (10 0.2 ) cm (d) (10 0.1 ) cm

Q35-If the temperature of a body increases from

28.6 0.1 0C to 79.4 0.10C, then the rise in thetemperature is

(a) 50.8 0.1 0C (b) 50.80C

(c) 50.8 0.2 0C (d) none of theseQ36-The period of oscillation of a simple pendulum is

T = 2 ( L /g)1/2. The value of L is about 10 cm and isknown to 1 mm accuracy. The period of oscillation is

about 0.5 s. The time of 100 oscillation is measured

with a wrist watch of 1 s resolution. What is the

accuracy in the determination of g?

(a) 5 % (b) 3 % (c) 2 % (d) 1 %

Q37- A physical quantity P is related to four

observables a,b,c and d as follows:

P = a3 b2/ ( dc). The percentage errors ofmeasurement in a , b, c and d are 1%, 3% , 4% and 2

% respectively. What is the percentage error in the

quantity P=..If the value of P calculated using theabove relation turns out to be 3.763, the value to

which one round off the resultis

Q38- The resistance R = V/ I where V = (100 5) volt

and I = (10 0.2) A. The percentage error in R will be(a) 3% (b) 7 % (c) 8% (d) none of these.

Q39- Two rods are of lengths 3.161 0.3 cm and

1.121 0.1 cm. Their combined length is

(a) 4.282 0.2 cm (b) 4.282 cm

(c) 4.282 0.4 cm (d) 4.282 0.1cm

Q40- 97 km-36.8 km (with proper significant figures) =

(a) 60.km (b) 60.2 km

(c) 61. km (d) none of these

Q41- A substance of mass 5.74 g occupies volume of

1.2 cm3.The density ( with proper significant figures) is

(a) 4.783 g/ cm3 (b) 4.78 g/ cm3

(c) 4.7830 g/ cm3 (d) 4.8 g/ cm3

Q42- Addition of 17.35 gm, 25.6 gm and 8.498 gm will

result ( with proper significant figures)

(a) 51.50gm (b) 51.5gm

(c) 51.54 gm (d) none of these

Q43- With proper significant figures, what is sum of

6.75 x 103 cm and 4.52 x 102 cm?

(a) 7.20x 103 cm (b) 7.00x 103 cm

(c) 7.202x 103 cm (d) none of these

Q44- Each side of a cube is measured to be 7.203 m.

With proper significant figures, what is the total surface

area?(a) 311.299 m2 (b) 311.300 m2

(c) 311.30 m2 (d) 311.3 m2

Q45- Rounded off value of 3.365 to two decimal places

equals to

Q46- The number of significant figures in 307000.m are

. and in 307000 are ..