Verified Solution • 2025–26 Session moderate

QJEEM21Phd5c0: JEE Main 2021 Physics - Class 12 JEEM21Phd5c0 Solution: Car B overtakes another car A at a relative speed of 40 ms 1 .…

Car B overtakes another car A at a relative speed of 40 ms −- 1. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when the car B is 1.9 m away from the car A?

Multiple Choice Options

  • A 4 ms −- 1
  • B 0.2 ms −- 1
  • C 40 ms −- 1
  • D 0.1 ms −- 1

Step-by-Step Verified Solution

Here, 1v+1u=1f{1 \over v} + {1 \over u} = {1 \over f} .......(1)

⇒\Rightarrow 1v+1−190=110{1 \over v} + {1 \over { - 190}} = {1 \over {10}}

⇒\Rightarrow v = 192{{19} \over 2}

Differentiating equation (1) w.r.t t we get

−1v2(dvdt)−1u2(dudt)=0- {1 \over {{v^2}}}\left( {{{dv} \over {dt}}} \right) - {1 \over {{u^2}}}\left( {{{du} \over {dt}}} \right) = 0

⇒\Rightarrow (dvdt)=−v2u2(dudt)\left( {{{dv} \over {dt}}} \right) = - {{{v^2}} \over {{u^2}}}\left( {{{du} \over {dt}}} \right)

⇒\Rightarrow (dvdt)=−(192190)2×40\left( {{{dv} \over {dt}}} \right) = - {\left( {{{{{19} \over 2}} \over {190}}} \right)^2} \times 40

=1400×40=0.1= {1 \over {400}} \times 40 = 0.1 m/s

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring