Question

A uniform rectangular plate of mass m which is free to rotate about the smooth vertical hinge

Answer 1

Explanation:

Angular momentum of the system above hinge should be.

Angular momentum of particle of mass m before collision is,

Lp=a.mu

Lp=mua

Let after collision the angular velocity of the attached system be ω

Moment of inertia about a perpendicular axis passing through hinge is

I= moment of inertia of particle of mass m about hinge + Moment of inertia of the plate about hinge.

m.(25a)+121m(a2+(2a)2)

=45ma2+125ma2

=1220ma2

Applying conservation of angular mamentum we get

Iw=Lp

=35ma2

35ma2.ω=mua

⇒5a3u

HOPE IT HELPS YOU BRO.