Units & Dimensions

JEE Main level, single correct, medium

39 of 149

Question 39 of 149

Given a charge qq, current I and permeability of vacuum μ0\mu_0. Which of the following quantity has the dimension of momentum?

Show answer and solution

Answer: (B) qμ0Iq \mu_0 I

Q=ATI=Aμ0=MLT−2 A−2P=Qxμ0yIz=[AT]x[MLT−2 A−2]y[A]zMLT−1=MyLyTx−2yA−2y+z+x Now; y=1x−2y=−1−2y+z=0∴x=y=z=1\begin{aligned} & \mathrm{Q}=\mathrm{AT} \\ & \mathrm{I}=\mathrm{A} \\ & \mu_0=\mathrm{MLT}^{-2} \mathrm{~A}^{-2} \\ & \mathrm{P}=\mathrm{Q}^{\mathrm{x}} \mu_0^{\mathrm{y}} \mathrm{I}^{\mathrm{z}}=[\mathrm{AT}]^{\mathrm{x}}\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]^{\mathrm{y}}[\mathrm{A}]^{\mathrm{z}} \\ & \mathrm{MLT}^{-1}=\mathrm{M}^{\mathrm{y}} \mathrm{L}^{\mathrm{y}} \mathrm{T}^{\mathrm{x}-2 \mathrm{y}} \mathrm{A}^{-2 \mathrm{y}+\mathrm{z+x}} \\ & \text { Now; } \mathrm{y}=1 \\ & \mathrm{x}-2 \mathrm{y}=-1 \\ & -2 \mathrm{y}+\mathrm{z}=0 \\ & \therefore \mathrm{x}=\mathrm{y}=\mathrm{z}=1\end{aligned}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

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.