Of the following quantities, which one has dimensions different from the remaining three 

(1) Energy per unit volume

(2) Force per unit area

(3) Product of voltage and charge per unit volume

(4) Angular momentum per unit mass

Subtopic:  Dimensions |
 65%
From NCERT
AIIMS - 1987
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A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented by 

(1) mr26πη

(b) 6πmrηg2

(c) m6πηrv

(4) None of the above

Subtopic:  Dimensions |
From NCERT
AIIMS - 1987
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The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f=CmxKy; where C is a dimensionless quantity. The value of x and y are 

1. x=12,y=12

2. x=12,y=12

3. x=12,y=12

4. x=12,y=12

Subtopic:  Dimensions |
 61%
From NCERT
PMT - 1990
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The quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of

1. Pressure

2. Work

3. Latent heat

4. None of the above

Subtopic:  Dimensions |
From NCERT
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The velocity of water waves v may depend upon their wavelength λ, the density of water ρ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as: 

1. v2-1ρ-1

2. v2gλρ

3. v2

4. v2g1λ3

Subtopic:  Dimensions |
 65%
From NCERT
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The dimensions of resistivity in terms of \(M\), \(L\), \(T\), and \(Q\) where \(Q\) stands for the dimensions of charge, will be:
1. \(\left[M L^3 T^{-1} Q^{-2}\right]\)
2. \(\left[M L^3 T^{-2} Q^{-1}\right]\)
3. \(\left[M L^2 T^{-1} Q^{-1}\right]\)
4. \(\left[M L T^{-1} Q^{-1}\right]\)

Subtopic:  Dimensions |
 63%
From NCERT
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The dimensions of Farad are , where Q represents electric charge [This question includes concepts from 12th syllabus]

(1) M1L2T2Q2

(2) M1L2TQ

(3) M1L2T2Q

(4) M1L2TQ2

Subtopic:  Dimensions |
 68%
From NCERT
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The equation of a wave is given by Y=Asinω(xvk) where ω is the angular velocity, x is length and v is the linear velocity. The dimension of k is 

(1) LT

(2) T

(3) T1

(4) T2

Subtopic:  Dimensions |
 70%
From NCERT
PMT - 1993
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Dimensional formula of capacitance is 

(1) M1L2T4A2

(2) ML2T4A2

(3) MLT4A2

(4) M1L2T4A2

Subtopic:  Dimensions |
 71%
From NCERT
PMT - 1978
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Dimensional formula of heat energy is  

(1) ML2T2

(2) MLT1

(3) M0L0T2

(4) None of these

Subtopic:  Dimensions |
 84%
From NCERT
PMT - 1976
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