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(A) To find the pair with different dimensions,we analyze each option:$A$. Linear momentum = $	ext{Mass} 	imes 	ext{Velocity} = [M L T^{-1}]$. Mome

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Linear momentum and moment of a force

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(A) To find the pair with different dimensions,we analyze each option:$A$. Linear momentum = $	ext{Mass} 	imes 	ext{Velocity} = [M L T^{-1}]$. Moment of a force (Torque) = $	ext{Force} 	imes 	ext{Distance} = [M L T^{-2}] 	imes [L] = [M L^2 T^{-2}]$. These have different dimensions.$B$. Planck's constant $(h)$ has dimensions $[M L^2 T^{-1}]$. Angular momentum $(L = mvr)$ has dimensions $[M] 	imes [L T^{-1}] 	imes [L] = [M L^2 T^{-1}]$. These have the same dimensions.$C$. Pressure = $	ext{Force} / 	ext{Area} = [M L T^{-2}] / [L^2] = [M L^{-1} T^{-2}]$. Modulus of elasticity = $	ext{Stress} / 	ext{Strain} = [M L^{-1} T^{-2}] / [1] = [M L^{-1} T^{-2}]$. These have the same dimensions.$D$. Torque = $	ext{Force} 	imes 	ext{Distance} = [M L^2 T^{-2}]$. Potential energy = $	ext{Work} = [M L^2 T^{-2}]$. These have the same dimensions.Therefore,the correct option is $A$.

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

In the following list,the only pair which has different dimensions is

Similar Questions

Which of the following is the correct order of the fundamental forces in nature, arranged from weakest to strongest?

Identify the pair that has the same dimensions.

Match the following physical quantities with their respective dimensional formulas:
$(A)$ Thermal conductivity $(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant (ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat (iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat (iv) $M^0L^2T^{-2}$

The related effort to derive the properties of a bigger,more complex system from the properties and interactions of its constituent simpler parts is:

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