Show that mechanical energy of a body sliding down freely along a smooth inclined plane is conserved.

Show that the potential energy of a body raised vertically to a height h is the same as the potential energy of the body raised to the same height along a smooth inclined plane.

Prove that the work done by a body sliding down a smooth inclined plane , from a height h to the ground level, is the same as the work done in a free fall from the same height h to the ground .

A body is kept on a horizontal rough plane. The plane is then gradually raised to an inclination of 30^(@) with the horizontal and the body starts to slide down. The body descends 12 m along the inclined plane in the next 4 s. Find the coefficients of static and kinetic friction between the surfaces in contact.

A body is sliding down an inclined plane having coefficient of friction 0.5. If the normal reaction is twice that of the resultant downward force along the inclined plane , then find the angle between the inclined plane and the horizontal.

Height of the vertex of an inclined plane is h . From the vertex , a body is released along the inclined plane . Explain whether the kinetic energy of the body at the base of the inclined plane depends on the inclination.

Give the definition of coefficient of restitution .Prove that for perfect elastic collision of two bodies moving in the same line , the kinetic energy is conserved.