The time period of SHM is 8 sec. At what time from mean position kinetic energy becomes half of its potential energy.

A particle of mass 10 g executing SHM has a velocity of 6cm s^(-1) after one second of its starting from the mean position. If the time period is 6 seconds, find its maximum kinetic energy.

Prove that the sum of potential and kinetic energies of a body in SHM is constant

When an air bubble rise in water, what happens to its potential energy?

The kinetic energy of an object of mass, m moving with a elocity of 5 ms^-1 , is 25J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

A body is projected such that its kinetic energy at the top of its trajectory is frac(3)(4) of its initial kinetic energy. What is the angle of projection of the projectile?

Work done by a body against friction always results in a loss of its kinetic/ potential energy.

A point particle of mass 0.1kg is excecuting SHM of amplitude 0.1m. When the particle passes through the mean position, its kinetic energy is 8xx10^(-3) J. Obtain the equation of motion of the particle if the initial phase’of oscillation is 45^@ .

A person trying to lose weight (dieter) lifts a 10 kg mass, one , thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated, (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 xx 10^7 J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?