The dimensions of the quantities in one of the following pairs are the same. Identify the pairs.

Question

The dimensions of the quantities in one of the following pairs are the same. Identify the pairs. (A) Torque and work (B) Angular momentum and work (C) Energy and Youngs modulus (D) Light year and time

Tardigrade Admin · Accepted Answer

Torque is defined as product of force into perpendicular distance from axis of rotation.

τ = F \times r

∴

Dimensions of

τ = [M L T^{- 2}] [L]

= [M L^{2} T^{- 2}]

Also, work

=

force

\times

displacement Work

= [M L T^{- 2}] [L] = [M L^{2} T^{- 2}]

Hence, work and torque have same dimensions.

Q. The dimensions of the quantities in one of the following pairs are the same. Identify the pairs.

Torque and work

Angular momentum and work

Energy and Youngs modulus

Light year and time

Torque is defined as product of force into perpendicular distance from axis of rotation. τ=F×r ∴ Dimensions of τ=[MLT−2][L] =[ML2T−2] Also, work = force × displacement Work =[MLT−2][L]=[ML2T−2] Hence, work and torque have same dimensions.