Correct Answer - Option 4 : Acceleration
CONCEPT:
Dimensions
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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.