At a certain speed of bus, its whole body starts vibrating strongly. Explain.

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^2=(2gh)/(1+k^2//R^2) using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = 2xx10^30 kg ).

Why does a body regain its shape or size when deforming forces are removed? Explain it on the basis of atomic view of elasticity.

A body of mass 0.40 kg moving initially with a constant speed of 10 m s^-1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = -5 s, 25 s, 100 s.

A body is projected in vertically upwards direction with a speed u. Find the distance travelled by the body in reaching its topmost point.