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 |
 64%
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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The dimensions of coefficient of thermal conductivity is 

(1) ML2T2K1

(2) MLT3K1

(3) MLT2K1

(4) MLT3K

Subtopic:  Dimensions |
 63%
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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