A stone attached to a rope of length l = 80 cm is rotated with a speed of 240 r.p.m. At the moment when the velocity is directed vertically upwards, the rope breaks. To what height does the stone rise further?

A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because

The K.E. (K) of a particle moving along a circle of radius r depends upon the distance covered (s) as K = as². The centripetal force acting on the particle is given by

A particle moves in a circular path of radius r, in half of its period. Its displacement and distance covered are,

A stone of mass 250 gram, attached at the end of a string of length 1.25 m is whirled in a horizontal circle at a speed of 5 m/s. What is the tension in the string?

A motor cyclist loops a vertical circular loop of diameter 18 m, without dropping down, even at the highest point of the loop. What should be his minimum speed at the lowest point of the loop?

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the outer end is

A weightless thread can bear tension upto 3.7 kg weight. A stone of mass 500 gram is tied at its one end and revolved in a vertical circular path of radius 4 m. If g = 10 m/s², then the maximum angular velocity of the stone is (radians/sec) will be

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two seconds, it rotates through θ₁ and in next two seconds, it rotates through θ₂. What is the ratio θ₂ / θ₁?

What is the smallest radius of a curve on a horizontal road, at which a cyclist can travel if his speed is 36 km/hour and the angle of inclination is 45°? (g = 10 m/s²)