A large mass M and a small mass m hang at the two ends of a string that passes through a smooth tube as shown in Fig. The mass m moves around a circular path in a horizontal plane. The length of the string from mass m to the top of the tube is l and ϴ is the angle the string makes with the vertical. What should be the frequency (ν) of rotation of mass m so that mass M remains stationary?
A block slides down a smooth inclined plane to the ground when released at the top, in time t seconds. Another block is dropped vertically from the same point, in the absence of the inclined plane and reaches the ground in t/2 second. Then the angle of inclination of the plane with the vertical is
A lump of clay of mass 10 g travelling with a velocity 10 cm/sec, towards east collides head on with another lump of clay of mass 10 g travelling with velocity of 20 cm/sec towards west. If the two lumps coalesce after collision, what is its velocity if no external force acts on the system?
Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg weight is attached to rope at the mid-point which now no more remains horizontal. The minimum tension required to completely straighten the rope is
A small cart with a sphere suspended over it by a string (see Fig.) approaches an inclined plane at a speed V. In which direction with respect to the vertical will the string supporting the sphere be deflected when the cart begins to climb the inclined plane
