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Question

Physics Question on Dimensional Analysis

The dimensions of angular momentum, latent heat and capacitance are, respectively.

A

ML2T1A2,L2T−2,M−2L−2T2ML^2T^1A^2, L^2T^{-2}, M^{-2}L^{-2}T^2

B

ML2T−1,L2T−2,M−1L−2T4AML^2T^{-1}, L^2T^{-2}, M^{-1}L^{-2}T^4A

C

ML2T−2,L2T−2,ML2TA2ML^2T^{-2}, L^2T^{-2}, ML^{2}TA^2

D

ML2T−1,L2T−2,M−1L−2T4A2ML^2T^{-1}, L^2T^{-2}, M^{-1}L^{-2}T^4A^2

Answer

ML2T−1,L2T−2,M−1L−2T4A2ML^2T^{-1}, L^2T^{-2}, M^{-1}L^{-2}T^4A^2

Explanation

Solution

Angular momentum =m×v×r=m\times v\times r =ML2T−1=ML^{2}T^{-1} Latent heat L=Qm=ML2T−2M=L2T−2L=\frac{Q}{m}=\frac{ML^{2}T^{-2}}{M}=L^{2}T^{-2} Capacitance C=ChargeP.d.=M−1L−2T4A2C=\frac{Charge}{P.d.}=M^{-1}L^{-2}T^{4}A^{2}