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Question: The dimensions of physical quantity \(X\) in the equation Force \(= \frac{X}{\text{Density}}\) is gi...

The dimensions of physical quantity XX in the equation Force =XDensity= \frac{X}{\text{Density}} is given by

A

M1L4T−2M^{1}L^{4}T^{- 2}

B

M2L−2T−1M^{2}L^{- 2}T^{- 1}

C

M2L−2T−2M^{2}L^{- 2}T^{- 2}

D

M1L−2T−1M^{1}L^{- 2}T^{- 1}

Answer

M2L−2T−2M^{2}L^{- 2}T^{- 2}

Explanation

Solution

[X] = [F] × [ρ] = [MLT−2]×[ML3]=[M2L−2T−2]\lbrack MLT^{- 2}\rbrack \times \left\lbrack \frac{M}{L^{3}} \right\rbrack = \lbrack M^{2}L^{- 2}T^{- 2}\rbrack