Question

a uniform rod ab which is free to swing in the vertical plane about a horizontal axis

Answer 1

Explanation:

186098 - A uniform rod AB which is free to swing in t-askIITians. A uniform rod AB which is free to swing in the vertical plane about a horizontal axis through A, is hanging freely. A particle of equal mass strikes the rod with a velocity v and gets stuck to it. · 

Answer 2

The angular velocity is - 3V0/4l

Let the rod AB hangs vertically so that the axis of rotation is passing through the end A.

Let the length of the rod be = L.

Since, initially the rod is at rest and the particle is moving with a velocity V0.

Therefore, the initial angular momentum of system -

Li = mV0L

Lf = Irod + Iparticle × ω

= 1/3 mL² + mL² × ω

= 4/3 mL²ω

According to conservation of the angular momentum -

Li = Lf

4/3 mL²ω = mV0L

ω = 3V0/4l