JEE Main 2020PhysicsCenter of Mass Momentum and CollisionMediumMCQ

JEE Main 2020 — Center of Mass Momentum and Collision Question with Solution

JEE Main 2020 (09 Jan Shift 2)

Question

A rod of length l has non-uniform linear mass density given by ρx=a+bxl2, where a and b are constants and 0≤x≤l The value of x for the centre of mass of the rod is at:

Choose an option

Show full solutionCorrect option: B
Correct answer
B342a+b3a+bL

Step-by-step explanation


Xcm=1M∫0ιx.dM
dM=ρ.dx=a+bxı2.dx
xcm=∫xdM∫dm=∫xρdx∫ρdx=∫0ιxa+bx2ι2dx∫0ιa+bx2ι2dx
=ax220ι+bι2x440ιax0ι+bι2x330ι
=aι22+bι24aι+bι3=2a+b3a+bι4×3
=3ι42a+b3a+b

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About this question

This is a previous-year question from JEE Main 2020, covering the Center of Mass Momentum and Collision chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.