A solid sphere rolls without slipping down an inclined plane of angle $heta$. What fraction of its total kinetic energy is rotational?

If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. of the body at the contact ($g = 10\;m/{s^2}$)

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by

An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

A 16 kg block moving on a frictionless horizontal surface with a velocity of 4 m/s compresses an ideal spring and comes to rest. If the force constant of the spring be 100 N/m, then the spring is compressed by

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of ${60^0}$ with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be

A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to

A machine which is 75 percent efficient, uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in $m{s^{ - 1}}$)

If the water falls from a dam into a turbine wheel 19.6 m below, then the velocity of water at the turbine is ($g = 9.8\;m/{s^2}$)

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of ${60^0}$ with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be

A ball of mass 2 kg moving with velocity $3{\rm{\;m}}{{\rm{s}}^{ - 1}},$ collides with spring of natural length 2 m and force constant $144{\rm{\;N}}{{\rm{m}}^{ - 1}}.$ what will be length of compressed spring?