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Units & Dimensions

JEE Main level, single correct, medium

106 of 149

Question 106 of 149

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

Show answer and solution

Answer: (D) $\left[{t}^{-1}{v}^{-2}{l}^{1}\right]$

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

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

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

Comparing powers,

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

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

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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More Physics practice

JEE Main Physics practice question on Units & Dimensions (Dimensions), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.

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

JEE Main question paper PDF

More Physics practice

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