Question

A block of mass m is placed at the top of a smooth wedge ABC. The wedge is rotated about an axis passing through C as shown in the figure. The minimum value of angular speed w such that the block does not slip on the wedge is-

• A. $\left( \sqrt{\frac{g\sin\theta}{\mathcal{l}}} \right)\sec\theta$
• B. $\left( \sqrt{\frac{g}{\mathcal{l}}} \right)\cos\theta$
• C. $\left( \sqrt{\frac{g}{\mathcal{l}\cos\theta}} \right)\cos\theta$
• D. $\sqrt{\frac{g\sin\theta}{\mathcal{l}}}$

Answer 1

Answer: (A)

$\left( \sqrt{\frac{g\sin\theta}{\mathcal{l}}} \right)\sec\theta$

Answer 2

mw²r cos q = mg sin q

mw²l cos² q = mg sin q

w=$\sqrt{\frac{g\sin\theta}{\mathcal{l}\cos^{2}\theta}}$=$\sqrt{\frac{g\sin\theta}{\mathcal{l}}}$secq