Question

A particle of mass $ m $ is initially situated at point $ P $ inside a hemispherical surface of radius $ r $ as shown in the figure.

A horizontal acceleration of magnitude $ a_0 $ is suddenly produced on the particle in the horizontal direction. If gravitational acceleration is neglected, then time taken by the particle to touch the sphere again is

• A. $ \sqrt{\frac{4r\,sin\,\alpha}{a_{0}}} $
• B. $ \sqrt{\frac{4r\,tan\,\alpha}{a_{0}}} $
• C. $ \sqrt{\frac{4r\,cos\,\alpha}{a_{0}}} $
• D. None of these

Answer 1

Answer: (C)

$ s=2r\,cos\,\alpha $
$ \because s=\frac{1}{2}a_{0}t^{2} $ or $ 2r\,cos\,\alpha=\frac{1}{2}a_{0}t^{2} $

$ \therefore t=\sqrt{\frac{4r\,cos\,\alpha}{a_{0}}} $