Which physical quantities have the same dimen | vedclass

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Question

(A) The dimension of a physical quantity is given by the powers to which the fundamental units are raised.$(a)$ Couple of force (Torque) = $|\overrigh

Vedclass · Accepted Answer

Couple of force and work

Vedclass · Answer

(A) The dimension of a physical quantity is given by the powers to which the fundamental units are raised.$(a)$ Couple of force (Torque) = $|\overrightarrow r 	imes \overrightarrow F | = [M^1 L^2 T^{-2}]$Work = $|\vec F \cdot \vec d| = [M^1 L^2 T^{-2}]$Since both have the same dimensional formula $[M^1 L^2 T^{-2}]$,they have the same dimension.$(b)$ Force = $[M^1 L^1 T^{-2}]$,Power = $[M^1 L^2 T^{-3}]$. They are different.$(c)$ Latent heat = $[L^2 T^{-2}]$,Specific heat = $[L^2 T^{-2} K^{-1}]$. They are different.$(d)$ Work = $[M^1 L^2 T^{-2}]$,Power = $[M^1 L^2 T^{-3}]$. They are different.Therefore,the correct option is $A$.

List-$I$	List-$II$
$(a)$ ${R}_{H}$ (Rydberg constant)	$(i)$ ${kg} {m}^{-1} {s}^{-1}$
$(b)$ $h$ (Planck's constant)	$(ii)$ ${kg} {m}^{2} {s}^{-1}$
$(c)$ $u_{B}$ (Magnetic field energy density)	$(iii)$ ${m}^{-1}$
$(d)$ $\eta$ (Coefficient of viscosity)	$(iv)$ ${kg} {m}^{-1} {s}^{-2}$

Which physical quantities have the same dimension?

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