Question

A rod of mass M and length L is hinged about one of its end about horizontal axis . A particle of mass M/2 moving with speed v hits and sticks to the lower end . Find maximum deflection of the rod .​

Answer 1

Answer:

$\huge\underline\mathfrak\purple{Answer}$

At horizontal position the reaction 'N'.Let the mass of rod is m.The moment of inertia of rod about the axis passig through the end and perpendicular to its plane isI= 1/3 ml²

For rotation of rod,Moment of force = Applied torque

⟹x×F=Iα

⟹α= xF/1/3ml²

. =3xF/ml²

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Here α is angular acceleration about hinge .The position of centre of mass is aat the middle.So the linear acceleration of centre of mass,

a=α1/2

a=3xF/2ml

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So, the net force in vertical on centre of mass is =ma=3xF/21

This should be equal to N.

So, N= 3xF/21

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I hope this helps you......