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Question

Physics Question on Dimensional Analysis

The dimensions of kinetic energy is:

A

[M2L2T1][{{M}^{2}}{{L}^{2}}{{T}^{1}}]

B

[M1L2T1][{{M}^{1}}{{L}^{2}}{{T}^{1}}]

C

[M1L2T−2][{{M}^{1}}{{L}^{2}}{{T}^{-2}}]

D

[M1L2T−1][{{M}^{1}}{{L}^{2}}{{T}^{-1}}]

Answer

[M1L2T−2][{{M}^{1}}{{L}^{2}}{{T}^{-2}}]

Explanation

Solution

KE=12mv2KE=\frac{1}{2}m{{v}^{2}} ∴\therefore [KE]=[M][LT−1]2[ML2T−2][KE]=[M]{{[L{{T}^{-1}}]}^{2}}[M{{L}^{2}}{{T}^{-2}}]