Question

A thin uniform rod of mass m and length is rotating
at 70 rpm about a vertical axis passing through its
centre and perpendicular lo ils length. If two point
masses each of mass "m" are gently connected to the
ends of the rod, its rotational speed will become​

Answer 1

Explanation:

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 is

I=31ml2

For rotation of rod,

Moment of force = Applied torque

⟹x×F=Iα

⟹α=31ml2xF=ml23xF

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=α2l

a=2ml3xF

So, the net force in vertical on centre of mass is 

=ma

=2l3xF

This should be equal to N.

So, N=2l3xF 

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