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Question

A point object of mass m moving horizontally hits the uniform solid disc and stick to it. The disc is resting on a horizontal frictionless surface and pivoted at its centre as shown in figure. Find out the MOI of the disc if it rotates with angular velocity ω=v5R after the strike.


A
I=mR22
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B
I=mR2
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C
I=4mR2
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D
I=32mR2
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Solution

The correct option is D I=32mR2
Given, mass of point object =m
Speed of point object =v
Angular momentum of object about disc centre before hitting the disc =mv(Rsin30)=mvR2


Hence, after hitting, angular momentum of the system (disc + particle) =I=(I+mR2)
From angular momentum conservation,
mvR2=(I+mR2)ω
mvR2=(I+mR2)v5R
5mR22mR2=I
I=3mR22

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