Q72 / 90 · JEE Main 2021 (20 Jul Shift 2) · Physics

If time $(t),$ velocity $(v),$ and angular momentum $(l)$ are taken as the fundamental units. Then the dimension of mass $(m)$ in terms of $t, v$ and $l$ is:

Solution

$m \propto t^{a} v^{b} ℓ^{c}$

$m \propto [T]^{a} {[{LT}^{- 1}]}^{b} {[{ML}^{2} T^{- 1}]}^{c}$

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

Comparing powers,

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

$m \propto t^{- 1} v^{- 2} ℓ^{1}$

Hence, the correct answer is option: 'D'.