Question

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:

• A. $\frac{12u}{5a}$
• B. $\frac{12u}{19a}$
• C. $\frac{3u}{2a}$
• D. $\frac{3u}{5a}$

Answer 1

Answer: (D)

$\frac{3u}{5a}$

Applying angular momentum cnservation,

$m.u.a=Iw$

$I=m(\frac{a^2}{12}+\frac{4a^2}{12})+m(a^2+\frac{a^2}{4})$

$I=\frac{5m{a}^2}{3}$

$\therefore m.u.a=\frac{5m{a}^2}{3}.w$

$w=\frac{3}{5}\frac{u}{a}$