Question

A rectangular door of mass \(18\,\mathrm{kg}\) and width \(90\,\mathrm{cm}\) is hinged at one end and can rotate about the vertical axis without friction. A bullet of mass \(15\,\mathrm{g}\) fired with a speed of \(450\,\mathrm{m\,s^{-1}}\) into the door gets embedded exactly at the center of the door. The angular speed of the door just after the bullet gets embedded is

• A. \(2.5~\mathrm{rad\,s^{-1}}\)
• B. \(0.625~\mathrm{rad\,s^{-1}}\)
• C. \(0.416~\mathrm{rad\,s^{-1}}\)
• D. \(1.25~\mathrm{rad\,s^{-1}}\)

Hint:

For perfectly inelastic rotational collisions, \[ \boxed{ mvr=I_{\text{final}}\omega } \] where \(I_{\text{final}}\) includes both the body and the embedded particle.

Answer 1

The Correct Option is B