JEE Main 2015PhysicsCenter of Mass Momentum and CollisionHardMCQ

JEE Main 2015 — Center of Mass Momentum and Collision Question with Solution

JEE Main 2015 (11 Apr Online)

Question

A uniform thin rod AB of length L has linear mass density μx=a+bxL, where x is measured from A. If the CM of the rod lies at a distance of 712L from A, then a and b are related as:

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Show full solutionCorrect option: A
Correct answer
A2a=b

Step-by-step explanation



Consider an infinitesimal small element of length dx and mars density λ

xcm=∫dmx∫dm=∫λ dxx∫λ dx

=∫0La+bLxxdx∫0La+bLxdx

=∫0Laxdx+∫0LbLx2dx∫0Ladx+∫0LbLxdx

=ax220L+bL x330Lax0L+bLx220L

=a2L2-02+b3L L3-03aL-0+b2LL2-02

=a2L2+bL23aL+bL2=a2L+bL3a+b2

∵xcm=7L12=a2+b3La+b2⇒712= 3a+2b62a+b2

⇒712=3a+2b3×12a+b⇒72a+b=43a+2b

⇒14a+7b=12a+8b⇒2a=b

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About this question

This is a previous-year question from JEE Main 2015, 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.