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(B) The dimensional formula of work is given by $[W] = [F] 	imes [s] = [MLT^{-2}][L] = [ML^2 T^{-2}]$.The dimensional formula of angular momentum is

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Work and torque

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(B) The dimensional formula of work is given by $[W] = [F] 	imes [s] = [MLT^{-2}][L] = [ML^2 T^{-2}]$.The dimensional formula of angular momentum is $[L] = [m][v][r] = [M][LT^{-1}][L] = [ML^2 T^{-1}]$.The dimensional formula of torque is $[	au] = [F] 	imes [r] = [MLT^{-2}][L] = [ML^2 T^{-2}]$.The dimensional formula of potential energy is $[U] = [m][g][h] = [M][LT^{-2}][L] = [ML^2 T^{-2}]$.The dimensional formula of linear momentum is $[p] = [m][v] = [M][LT^{-1}] = [MLT^{-1}]$.The dimensional formula of kinetic energy is $[K] = [M][v^2] = [M][LT^{-1}]^2 = [ML^2 T^{-2}]$.The dimensional formula of velocity is $[v] = [LT^{-1}]$.Comparing these,the dimensions of work and torque are both $[ML^2 T^{-2}]$. Therefore,option $B$ is correct.

$A$. Entropy	$I$. Angular velocity
$B$. Young's modulus of elasticity	$II$. Boltzmann constant
$C$. Angular momentum	$III$. Energy density
$D$. Decay constant	$IV$. Planck's constant

List-$I$	List-$II$
$(a)$ Torque	$(i)$ ${MLT}^{-1}$
$(b)$ Impulse	$(ii)$ ${MT}^{-2}$
$(c)$ Tension	$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension	$(iv)$ ${ML} {T}^{-2}$

Choose the physical quantity pair with the same dimensions.

Similar Questions

Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(a)$ Torque $(i)$ ${MLT}^{-1}$
$(b)$ Impulse $(ii)$ ${MT}^{-2}$
$(c)$ Tension $(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension $(iv)$ ${ML} {T}^{-2}$

Choose the most appropriate answer from the options given below:

Fill in the blanks:
$(a)$ $\frac{1\,\mu m}{1\,fm} = \,....$
$(b)$ The number of significant figures in $0.0060$ is $....$
$(c)$ To study nanotechnology,the $....$ microscope has been developed.

Which of the following pairs of physical quantities possess the same dimension?

The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

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