Question

Which of the following quantity has dimensional formula as that of \(\frac{Energy}{Mass\times Length}\) is:
1. Force
2. Power
3. Pressure
4. Acceleration

Answer 1

Correct Answer - Option 4 : Acceleration

CONCEPT:

Dimensions

• Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.

​EXPLANATION:

We know that the dimension of the energy is given as,

⇒ [Energy] = [M¹ L² T^-2]

So the dimension of \(\frac{Energy}{Mass\times Length}\) is given as,

\(⇒ \left [ \frac{Energy}{Mass\times Length} \right ]=\frac{\left [ M^{1}L^{2}T^{-2} \right ]}{[M^1L^1]}\)

\(⇒ \left [ \frac{Energy}{Mass\times Length} \right ]=[ M^{0}L^{1}T^{-2}]\)     -----(1)

The dimension of force is given as,

⇒ [F] = [M1 L1 T-2]     -----(2)

The dimension of power is given as,

⇒ [P] = [M1 L2 T-3]     -----(3)

The dimension of pressure is given as,

⇒ [P] = [M1 L-1 T-2]     -----(4)

The dimension of acceleration is given as,

⇒ [a] = [M0 L1 T-2]     -----(5)

• By the above explanation, it is clear that the dimensional formula for acceleration is the same as that of \(\frac{Energy}{Mass\times Length}\).
• Hence, option 4 is correct.