Rankers Physics

A uniform rectangular plate of mass m which is free to rotate about the smooth vertical hinge passing through the centre and perpendicular to the plate, is lying on a smooth horizontal surface. A particle of mass m moving with speed 'u' collides with the plate and sticks to it as shown in figure. The angular velocity of the plate after collision will be Image related to

\[ \frac{12u}{5a} \]
\[ \frac{12u}{19a} \]
\[ \frac{3u}{2a} \]
\[ \frac{3u}{5a} \]

Solution:

Taking rectangle and the object as one system angular momentum is conserved.

so,  mva= ( m(√5a/2)² + m((2a)²+ a²)/12) ω

\[ \omega = \frac{3u}{5a} \]

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