A toy gun fires a plastic pellet with a mass of $0.5\  g$. The pellet is propelled by a spring with a spring constant of $1.25\  N/cm$, which is compressed $2.0\  cm$ before firing. The plastic pellet travels horizontally $10\  cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\  N$. What is the speed (in $SI\  units$) of the bullet as it emerges from the barrel?

Mention the work done by spring force in cylic process.

A ball is dropped from a height of $80\,m$ on a surface which is at rest. Find the height attainded by ball after $2^{nd}$ collision if coefficient of restitution $e = 0.5$ ............ $\mathrm{m}$

A ball of mass $2 \,m$ and a system of two balls with equal masses $m$ connected by a massless spring, are placed on a smooth horizontal surface (see figure below). Initially, the ball of mass $2 \,m$ moves along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2 \,m$ is

A spring is compressed between two blocks of masses $m_1$ and $m_2$  placed on a horizontal frictionless surface as shown in the figure. When the blocks arc released, they have initial velocity of $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest. The ratio $\left( {\frac{{{x_1}}}{{{x_2}}}} \right)$ is

$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then