Total energy of an isolated system-

A large block of wood of mass $M=5.99 \mathrm{kg}$ is hanging from two long massless cords. A bullet of mass $m=10 \mathrm{g}$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards, their center of mass rising a vertical distance $h=9.8 \mathrm{cm}$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take $g=9.8{ \mathrm{m} \mathrm{s}}^{-2}$)

A sphere of mass $\text{'}m\text{'}$ is attached to a spring of spring constant $\text{'}k\text{'}$ and is held in unstretched position over an inclined plane as shown in the figure. After letting the sphere go, find the maximum length by which the spring extends, given the sphere only rolls.

A mass of $1 \mathrm{kg}$ falls from a height of $1 \mathrm{m}$ and lands on a mass less platform supported by a spring having spring constant $15 \mathrm{N} {\mathrm{m}}^{-1}$ as shown in the figure. The maximum compression of the spring is.
(acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

In the given figure, the block of mass $m$ is dropped from the point $A$. The expression for kinetic energy of block when it reaches point $B$ is

As per the given figure, two blocks each of mass $250 \mathrm{g}$ are connected to a spring of spring constant $2 \mathrm{N} {\mathrm{m}}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is

A mass of  $0.5 \mathrm{kg}$ moving with a speed of $1.5 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $\mathrm{k}=50 \mathrm{N} {\mathrm{m}}^{-1}$. The maximum compression of the spring would be