If time (t) , velocity (u) , and angular momentum (I) are taken as fundamental units. Then dimension

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1.Units, Dimensions and Measurement

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If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is

A

$[t^{-1} u^{-2}\,I^{1}]$

B

$[t^{1} u^{2}\,I^{-1}]$

C

$[t^{-2} u^{-1}\,I^{1}]$

D

$[t^{-1} u^{1}\,I^{-2}]$

(JEE MAIN-2021)

Solution

$m \propto t^{a} v^{b} \ell^{c}$

$m \propto[T]^{a}\left[L T^{-1}\right]^{b}\left[M L^{2} T^{-1}\right]^{c}$

$M^{1} L^{0} T^{0}=M^{c} L^{b+2 c} T^{a-b-c}$

comparing powers

$v=1, b=-2, a=-1$

$m \propto t^{-1} v^{-2} \ell^{1}$

Standard 11

Physics

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