Which One of the following pairs has the Same Dimensions?

Work and torque have the same dimensions. The dimensions of the work are Nm and for torque is Nm.

Why do Work and torque have the Same Dimensions

Dimensional Formula

It illustrates how to tie any unit to the basic units.

If we need to determine the dimensional formula for any quantity, we must first determine its units in terms of these basic units before substituting the dimensions for the units.

Work

Work is the result of force and displacement in the force's direction. The unit of work is the joule.

1 Joule = 1 N .1 m = N m

Unit of force is Newton (N), and the unit of distance is meter (m).

Torque

The definition of torque is the result of the force and the separation of the force from the site of action. Torque is measured in Newton meters or N m.

When two physical quantities have the same units, their dimensions will be the same as well.

Since work and torque share the same unit, their dimensions will likewise be the same.

The dimension of both is M L2 T-2. Work and torque have the same dimensions.

So, the correct answer is work and torque.

Summary:

Which One of the following pairs has the Same Dimensions?

The pair work and torque pair have the same dimensions. Nm is the dimension for both. The result of force and displacement in the force direction is work whereas the result of force separate from the action of the site is torque.