Identify the pair that has the same dimension | vedclass

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(A) The dimension of force is $[MLT^{-2}]$.The dimension of work is $[ML^2T^{-2}]$.The dimension of torque is defined as force multiplied by perpendic

Vedclass · Accepted Answer

Torque and Work

Vedclass · Answer

(A) The dimension of force is $[MLT^{-2}]$.The dimension of work is $[ML^2T^{-2}]$.The dimension of torque is defined as force multiplied by perpendicular distance,so its dimension is $[MLT^{-2}] 	imes [L] = [ML^2T^{-2}]$.The dimension of energy is the same as work,which is $[ML^2T^{-2}]$.The dimension of stress is defined as force per unit area,so its dimension is $[MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$.Comparing these,we see that torque and work have the same dimensions $[ML^2T^{-2}]$.Therefore,the correct pair is Torque and Work.

List-$I$	List-$II$
$A$. Spring constant	$I$. $ML^2 T^{-2} K^{-1}$
$B$. Thermal conductivity	$II$. $ML^0 T^{-2}$
$C$. Boltzmann constant	$III$. $ML^2 T^{-3} A^{-2}$
$D$. Inductive reactance	$IV$. $MLT^{-3} K^{-1}$

Identify the pair that has the same dimensions.

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