Test: Physical World, Units And Measurements - From Past 28 Years Questions


40 Questions MCQ Test Physics 28 Years Past year papers for NEET/AIPMT Class 11 | Test: Physical World, Units And Measurements - From Past 28 Years Questions


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QUESTION: 1

The dimensional formula for angular momentum is  [1988]

Solution:

[Angular momentum ] = [Momentum of inertia] × [Angular velocity] = ML2 × T–1
= ML2T–1

OR

In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.

In SI base units: kg m2 s−1

Dimension: M L2T−1

Derivations from other quantities: L = Iω = r × p

 

QUESTION: 2

If C and R denote capacitance and resistance, the dimensional formula of CR is [1988]

Solution:

CR = [M -1 L-2 T 4 A 2 ][M1 L2 T -3 A -2 ] = [T] = [M0 L0 T1]

QUESTION: 3

The dimensional formula of torque is [1989]

Solution:

ζ = [Force × distance] = [MLT–2] [L] = ML2T–2

QUESTION: 4

Dimensional formula of self inductance is [1989]

Solution:

Induced emf 

where L is the self inductance and  is the rate of change of current.

∴ Dimensional formula of  L = 

QUESTION: 5

Of the following quantities, which one has dimension different from the remaining three? [1989]

Solution:

For angular momentum, the dimensional formula is ML2T–1. For other three, it is ML-1T–2.

QUESTION: 6

If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the units of b is [1989]

Solution:

QUESTION: 7

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient ΔV/ΔZ is given by where η is constant called coefficient of viscosity. The dimensional formula of η is [1990]  

Solution:

Substitute the dimension al formula of F, A, ΔV and ΔZ on both sides and find that for η.

QUESTION: 8

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation of the type f = c mx ky, where c is a dimensionless constant. The values of x and y are 

Solution:

f = c mx ky; Spring constant k = force/length. [M0L0T–1] = [Mx (MT–2)y] =[ Mx + y T–2y]
 

⇒ x+y = 0, -2y = -1 or 

Therefore,  x = -

QUESTION: 9

The dimensional formula of pressure is [1990]

Solution:

[Pressure] = [Force] / [Area]

= ML–1T–2

QUESTION: 10

The dimension al formula for permeability µ is given by [1991]

Solution:

[n] = L–1,  [I] = A

QUESTION: 11

A certain body weighs 22.42 gm and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 gm and 0.1 cc. Then maximum error in the den sity will be [1991]

Solution:

D = M/V

 =2 %

QUESTION: 12

P represents radiation pressure, crepresents speed of light and S represents radiation energy striking unit area per sec. The non zero integers x, y, z such that Px Sy cz is dimensionless are [1992]

Solution:

Try out the given alter natives.
When x = 1, y = –1, z = 1

 = [M0L0T0]

QUESTION: 13

The time dependence of a physical quantity p is given by p = p0 exp (– αt2), where α is a constant and t is the time. The constant α [1993]

Solution:

In p = p0 exp (–αt2), αt2 dimension less

QUESTION: 14

urpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by  where v is the velocity of oil at a distance a from the axis of the tube. The dimensions of η are

Solution:

QUESTION: 15

In a vernier calliper N divisions of vernier scale coincides with (N – 1) divisions of main scale (in which length of one division is 1 mm). The least count of the instrument should be[1994]

Solution:

Least count = 1MSD – 1 VSD

(∵ N  VSD = (N – 1)MSD 

QUESTION: 16

In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalen t to [1994]

Solution:

[F] = MLT–2 = (10g) (10 cm) (0.1s)–2
= (10–2 kg) (10–1m) (10–1s)–2 = 10–1N.

QUESTION: 17

Which of the following is a dimensional constant? [1995]

Solution:

A quantity which has dimension s an d a constant value is called dimensional constant. Therefore, gravitational constant (G) is a dimensional constant.

QUESTION: 18

The percentage errors in the measurement of mass and speed are 2% and 3% respectively.The error in kinetic energy obtained by measuring mass and speed will be [1995]

Solution:

Percentage error in mass 

percentage error in speed 

Kinetic energy 

∴ Error in measurement of kinetic energy

By Binomial Function ,

 Reqd. error

∴ %age error = 8%.

QUESTION: 19

An equation is given as : 

where P = Pressure, V = Volume & θ = Absolute temperature. If a and b are constants, then dimensions of a will be [1996]

Solution:

According to the principle of homogeinity quantity with same dimension can be added or subtracted.
Hence, Dimension of P = Dimension of 

⇒ Dimension of  = Dimension of 

a = [M L5 T–2]

QUESTION: 20

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of den sity will be [1996]

Solution:

Density =

  

% error in density = % error in Mass + 3 (% error in length]                              
 = 4 + 3(3) = 13%

QUESTION: 21

Which of the following will have the dimensions of time           [1996]

Solution:

QUESTION: 22

The force F on a sphere of radius  a moving in a medium with velocity v is  given by F = 6πηav.The dimensions of η are [1997]

Solution:

F= 6πη av

= ML–1T–1

QUESTION: 23

The dimensional formula for magnetic flux is [1999]

Solution:

Dimension of magnetic flux = Dimension of voltage × Dimension of time = [ML2T–3A–1] [T]  = [ML2T–2A–1]

∵ Voltage =

QUESTION: 24

Which one of the following groups have quantities that do not have the same dimensions? [2000]

Solution:

Force has dimension [MLT–2] while impulse has dimension [MLT–1], both have different dimensions.

QUESTION: 25

The dimensions of Planck’s constant are same as    [2001]

Solution:

We know that E = hv

Angular momentum = Iω    
= [ML2][T–1] = [ML2T–1]

QUESTION: 26

The unit of the Stefan-Boltzmann's constant is   [2002]

Solution:

E = σAT4
E is energy dissipated per second.

QUESTION: 27

The unit of permittivity of free space, εo is  [2004]

Solution:

⇒ unit of εo is (coulomb)2/ newton -metre2

QUESTION: 28

The dimensions of universal gravitational constant are [1992, 2004]

Solution:

∴  dimension of G is  

= M–1L3T–2

QUESTION: 29

The ratio of the dimension of Planck’s constant and that of the moment of inertia has the dimension of [2005]

Solution:

QUESTION: 30

The velocity v of a particle at time t is given by where a, b and c are constant.The dimensions of a, b and c are respectively [2006]

Solution:

Dimension of  a. t = dimension of velocity a . t = LT-1 ⇒ a = LT-2
Dimension of c = dimension of t (two physical quantity of same dimension can only be added)

So, dimension of c = T

Dimension of   = Dimension of v

  

So, answer is LT–2, L & T

QUESTION: 31

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be [2007]

Solution:

Dimensions of Resistance,

QUESTION: 32

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: [2008]

Solution:

Error in the measurement of radius of a sphere = 2%

Volume of the sphere =

∴  Error in the volume =  

  = 3 × 2% = 6%

QUESTION: 33

Which two of the following five physical parameters have the same dimensions?
(A) Energy density [2008]
(B) Refractive index
(C) Dielectric constant
(D) Young’s modulus
(E) Magnetic field

Solution:

[Energy density] = 

[Young’s Modulus] = 

QUESTION: 34

If the dimensions of a physical quantity are given by Ma Lb Tc, then the physical quantity will be:

Solution:
QUESTION: 35

The dimension of  where ε0 is permittivity of free space and E is electric field, is:[2010]

Solution:

 represents energy density i.e., energy per unit volume.

QUESTION: 36

The dimensions of   are    [2011]

Solution:

, so, dimensions are [LTT–1].

QUESTION: 37

The density of material in CGS system of units is 4g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be [2011M]

Solution:

In CGS system,

The unit of mass is 100g and unit of length is 10 cm, so

density = 

= 40 unit

QUESTION: 38

The dimensions of (μ0ε0)–1/2 are : [2012M]

Solution:

: speed of light

where ε0 =  permittivity of free space

μ0 = permeability of free space

So dimension LT–1

QUESTION: 39

In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows error in P is [NEET 2013]

Solution:

100%.
= 3 × 1% + 2 × 2% + 3% + 4% = 14%

QUESTION: 40

The pair of quantities having same dimensions is [NEET Kar. 2013]

Solution:

Work = Force ×  displacement Torque = Force × force arm              

= mass × acceleration × length              

= [M] × [LT–2] × [L] = [M L2T–2]