The dimensional formula of work is
- A.M L T⁻²
- B.M L² T⁻²
- C.M L² T⁻³
- D.M L⁻¹ T⁻²
Show answer
Correct answer: B. M L² T⁻²
Explanation
The correct answer is B, M L² T⁻². Work is force multiplied by displacement. Force has the dimensions M L T⁻², and multiplying it by a length adds one more power of L, which gives M L² T⁻². Energy has the same dimensions as work, since energy is the capacity to do work, and so does torque.
Option A, M L T⁻², is the dimensional formula of force, and also of weight, which is a force. Option C, M L² T⁻³, belongs to power, since power is work divided by time and therefore carries one extra power of T in the denominator. Option D, M L⁻¹ T⁻², is the formula for pressure, which is force divided by area. Because work and torque share the same dimensions, dimensional analysis alone cannot tell them apart, a standard limitation of the method.