Two long smooth horizontal rails…

Two long smooth horizontal rails separated by L=0.5 m are joined at one end by a resistor R=2 Ω (rails and rod have negligible resistance). A uniform…

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Two long smooth horizontal rails separated by

L=0.5\ \mathrm{m}

are joined at one end by a resistor

R=2\ \Omega

(rails and rod have negligible resistance). A uniform vertical magnetic field

B=2\ \mathrm{T}

fills the region. A rod of mass

0.2\ \mathrm{kg}

lying across the rails is given an initial speed

10\ \mathrm{m\,s^{-1}}

along the rails and then left alone. Choose the correct statement(s).

A. The initial deceleration of the rod is $25\ \mathrm{m\,s^{-2}}$ .
B. The rod stops after travelling a total distance of $4\ \mathrm{m}$ .
C. By the time the speed of the rod has fallen to $5\ \mathrm{m\,s^{-1}}$ , the heat generated in the resistor is $5\ \mathrm{J}$ .
D. The total charge that flows through the resistor is $2\ \mathrm{C}$ .

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Answer: A, B, D

The induced emf is

BLv

, so the retarding force is

B^2L^2v/R

. (A) At

v=10

F=\dfrac{(2)^2(0.5)^2(10)}{2}=5\ \mathrm{N}

and

a=F/m=25\ \mathrm{m\,s^{-2}}

: true. (B) Momentum equation

m\,dv=-\dfrac{B^2L^2}{R}dx

gives total distance

x=\dfrac{mv_0R}{B^2L^2}=\dfrac{0.2\times10\times2}{1}=4\ \mathrm{m}

: true. (C) The heat equals the kinetic energy lost,

\tfrac12(0.2)(100-25)=7.5\ \mathrm{J}

, not

5\ \mathrm{J}

: false. (D) Charge

q=\dfrac{BLx}{R}=\dfrac{2\times0.5\times4}{2}=2\ \mathrm{C}

(equivalently the impulse

mv_0=BLq=1\ \mathrm{N\,s}

gives

q=2

C): true.

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Original question written in the JEE Advanced 2025 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake