Dimensions of frequency are 

(1) M0L1T0

(2) M0L0T1

(3) M0L0T

(4) MT2

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Which one has the dimensions different from the remaining three

(1) Power

(2) Work

(3) Torque

(4) Energy

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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 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 

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The quantity X=ε0LVt:ε0 is the permittivity of free space, Lis length, V is potential difference and t is time. The dimensions of X are same as that of  

(1) Resistance

(2) Charge

(3) Voltage

(4) Current

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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

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The expression [ML2T2] represents

(1) Pressure

(2) Kinetic energy

(3) Momentum

(4) Power

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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

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The dimensions of CV2 matches with the dimensions of 

(1) L2I

(2) L2I 2

(3) LI2

(4) 1LI

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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

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The dimension of 1ε0μ0 is that of 

(1) Velocity

(2) Time

(3) Capacitance

(4) Distance

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