Consider a frictionless ramp on which a smooth object is made to slide down from an initial height $h$. The distance $d$ necessary to stop the object on a flat track (of coefficient of friction $\mu$),kept at the ramp end,is:

Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into

Two bodies $A$ and $B$ of masses $5.00 \ kg$ and $10.0 \ kg$ respectively,moving in opposite directions with velocities $4.00 \ m/s$ and $0.50 \ m/s$ respectively,make a head-on collision in free space. The force of their mutual interaction varies according to the given graph. The coefficient of restitution is

Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

$A$ particle is projected vertically upwards with a speed of $16 \ m/s$. After some time,when it again passes through the point of projection,its speed is found to be $8 \ m/s$. It is known that the work done by air resistance is the same during upward and downward motion. Then the maximum height attained by the particle is ...................... $m$ $(g = 10 \ m/s^2)$.

Two bodies of different masses $m_1$ and $m_2$ have equal momenta. Their kinetic energies $E_1$ and $E_2$ are in the ratio: