A ball is dropped from rest at a height of $60 \mathrm{m}$. On striking the ground, it loses $25\%$ of its energy. To what height does it rebound?

A bullet of mass $20 \mathrm{g}$ strikes a block of mass $980 \mathrm{g}$ with a velocity $v$ and is embedded in it. The block is in contact of a spring whose force-constant is $100 \mathrm{N}/\mathrm{m}$. After the collision the spring is compressed up to $10 \mathrm{cm}$.

Find the velocity of the block after the collision.

A bullet of mass $20 \mathrm{g}$ strikes a block of mass $980 \mathrm{g}$ with a velocity $v$ and is embedded in it. The block is in contact of a spring whose force-constant is $100 \mathrm{N}/\mathrm{m}$. After the collision the spring is compressed up to $10 \mathrm{cm}$.

Find the magnitude of the velocity $v$ of the bullet.

A bullet of mass $20 \mathrm{g}$ strikes a block of mass $980 \mathrm{g}$ with a velocity $v$ and is embedded in it. The block is in contact of a spring whose force-constant is $100 \mathrm{N}/\mathrm{m}$. After the collision, the spring is compressed up to $10 \mathrm{cm}$. Find loss in the kinetic energy due to the collision.

A smooth sphere (mass $10 \mathrm{kg}$) rolls on a smooth curved surface from the point A with a speed of $10 \mathrm{m}/\mathrm{s}$. The sphere reaches point D passing through point B. Find the total energy of the sphere at point A. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)