A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30$$^\circ$$, then the angle of inclination of plane B must be (approximately)
Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a square of side $$b$$. Moment of inertia of the system about an axis along one of the sides of the square is
If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of inertia.
A sphere of mass m is attached to a spring of spring constant k and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.
