A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity η. After some time the velocity of the ball attains a constant value known as terminal velocity vT. The terminal velocity depends on (i) the mass of the ball m, (ii) η, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?

1. vTmgηr

2. vTηrmg

3. vTηrmg

4. vTmgrη 

Subtopic:  Dimensions |
 55%
From NCERT
PMT - 1992
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The quantity X=ε0LVt; ε0 is the permittivity of free space, is length, V is the potential difference and t is time. The dimensions of X are the same as that of:

1. Resistance

2. Charge

3. Voltage

4. Current

Subtopic:  Dimensions |
 53%
From NCERT
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μ0 and ε0 denote the permeability and permittivity of free space, the dimensions of μ0ε0 are:

(1) LT1

(2) L2T2

(3) M1L3Q2T2

(4) M1L3I2T2

Subtopic:  Dimensions |
 67%
From NCERT
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The expression [ML2T2] represents

(1) Pressure

(2) Kinetic energy

(3) Momentum

(4) Power

Subtopic:  Dimensions |
 84%
From NCERT
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The dimensions of physical quantity X in the equation Force =XDensity is given by 

(1) M1L4T2

(2) M2L2T1

(3) M2L2T2

(4) M1L2T1

Subtopic:  Dimensions |
 78%
From NCERT
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The dimensions of CV2 matches with the dimensions of 

(1) L2I

(2) L2I 2

(3) LI2

(4) 1LI

Subtopic:  Dimensions |
 77%
From NCERT
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The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are 

(1) [FT2]

(2) [F1T2]

(3) [F1A2T1]

(4) [AT2]

Subtopic:  Dimensions |
 71%
From NCERT
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The dimension of 1ε0μ0 is that of 

(1) Velocity

(2) Time

(3) Capacitance

(4) Distance

Subtopic:  Dimensions |
 76%
From NCERT
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An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle?

(1) MLT2

(2) ML2T2

(3) MLT2

(4) L

Subtopic:  Dimensions |
 65%
From NCERT
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The dimensional formula of wave number is

(1) M0L0T1

(2) M0L1T0

(3) M1L1T0

(4) M0L0T0

Subtopic:  Dimensions |
 71%
From NCERT
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