Which of the following pair does not have same dimensions ?

Pressure, Modulus of Elasticity

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Angular velocity, Velocity gradient

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Surface tension, Force constant

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Impulse, Torque

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Solution

The correct option is A Impulse, Torque
Pressure $=$ Modulus of Elasticity $= \frac{F}{A} = M^{1} L^{- 1} T^{- 2}$
Angular velocity $= ω = T^{- 1}$
Velocity gradient $= \frac{d v}{d z} = \frac{L T^{- 1}}{L} = T^{- 1}$
Surface Tenstion $= \frac{f}{l} =$ Force constant $= \frac{M^{1} L^{1} T^{- 2}}{L^{1}} = M T^{- 2}$
Impulse $= f \times t = M^{1} L^{1} T^{- 2} \times T^{1} = M^{1} L^{1} T^{- 1}$
Torque $= \to r \times \to f = L^{1} \times M^{1} L^{1} T^{- 2} = M^{1} L^{2} T^{- 2}$
Hence, option D is correct.

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