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

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Torque and Work

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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 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-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

Identify the pair that has the same dimensions.

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