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

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

J & K CETJ & K CET 2002

Solution:

Torque is defined as product of force into perpendicular distance from axis of rotation.
$\tau=F \times r$
$\therefore $ Dimensions of $\tau=\left[M L T^{-2}\right][L]$
$=\left[M L^{2} T^{-2}\right]$
Also, work $=$ force $\times$ displacement Work
$=\left[M L T^{-2}\right][L]=\left[M L^{2} T^{-2}\right]$
Hence, work and torque have same dimensions.