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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Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful 

(1) A/B

(2) A + B

(3) AB

(4) None

Subtopic:  Dimensions |
 81%
From NCERT
PMT - 1997
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A force F is given by F = at + bt2, where t is time. What are the dimensions of a and b 

(1) MLT3 and ML2T4

(2) MLT3 and MLT4

(3) MLT1 and MLT0

(4) MLT4 and MLT1

Subtopic:  Dimensions |
 81%
From NCERT
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