The dimensions of torque are the same as that | vedclass

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(A) The dimensional formula for torque is given by $	au = r 	imes F$. Since the dimensions of force $F$ are $[M^1L^1T^{-2}]$ and the dimensions of d

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moment of force

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(A) The dimensional formula for torque is given by $	au = r 	imes F$. Since the dimensions of force $F$ are $[M^1L^1T^{-2}]$ and the dimensions of distance $r$ are $[L^1]$,the dimensions of torque are $[M^1L^1T^{-2}] 	imes [L^1] = [M^1L^2T^{-2}]$. The moment of force is defined as the product of force and the perpendicular distance from the axis of rotation,which is identical to the definition of torque. Therefore,the dimensions of the moment of force are also $[M^1L^2T^{-2}]$. Thus,the dimensions of torque are the same as those of the moment of force.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

The dimensions of torque are the same as that of

Similar Questions

Which of the following quantities has the same dimensions as that of energy?

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Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

Given below are two statements :
$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements,choose the correct answer from the options given below :

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