A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in the figure below. The coefficient of friction is $$\mu $$. If $$\mu < \tan \theta $$, then the time taken by the block to reach anorher point $$Q$$ on the inclined plane, where $$PQ=S,$$ is

If point A is in equilibrium under the action of the applied forces, the values of tensions and T _AB and T_AC are respectively.

A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3m/s, while the barrel is swinging upwards with a constant angular velocity of 2 rad/sec. The magnitude of the absolute velocity of the shell is

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately