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 type \(f= Cm^{x}k^{y}\); where \(C\) is a dimensionless quantity. The values of \(x\) and \(y\) will be:
1. \(x=\frac{1}{2},~y= \frac{1}{2}\)
2. \(x=-\frac{1}{2},~y= -\frac{1}{2}\)
3. \(x=\frac{1}{2},~y= -\frac{1}{2}\)
4. \(x=-\frac{1}{2},~y= \frac{1}{2}\)

Subtopic:  Dimensions |
 67%
From NCERT
PMT - 1990
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The quantities \(A\) and \(B\) are related by the relation, \(m= \frac{A}{B}\), 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) v2gλ-1ρ-1

(2) v2gλρ

(3) v2gλ

(4) v2g1λ3

Subtopic:  Dimensions |
 71%
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 |
 75%
From NCERT
PMT - 1993
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The period of a body under SHM i.e. presented by T=PaDbSc; where P is pressure, D is density and S is surface tension. The value of a, b and c are 

(1) 32,12,1

(2) 1,2,3

(3) 12,32,12

(4) 1,2,13

Subtopic:  Dimensions |
 64%
From NCERT
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The velocity of a freely falling body changes as gphq where g is acceleration due to gravity and h is the height. The values of p and q are 

(1) 1,12

(2) 12,12

(3) 12,1

(4) 1, 1

Subtopic:  Dimensions |
 86%
From NCERT
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 A small steel ball of radius \(r\) is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity \(\eta\). After some time the velocity of the ball attains a constant value known as terminal velocity \(v_T\). The terminal velocity depends on \((\text{i})\) the mass of the ball \(m\) \((\text{ii})\) \(\eta\) \((\text{iii})\) \(r\) and \((\text{iv})\) acceleration due to gravity \(g\). Which of the following relations is dimensionally correct:
1. \(v_T \propto \frac{mg}{\eta r}\)
2. \(v_T \propto \frac{\eta r}{mg}\)
3. \(v_T \propto \eta rmg\)
4. \(v_T \propto \frac{mgr}{\eta }\)

Subtopic:  Dimensions |
 61%
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 |
 57%
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 |
 84%
From NCERT
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