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
$1$
$\frac{4}{9}$
$\frac{1}{2}$
$\frac{2}{3}$
A bullet of mass $m$ strikes a block of mass $M$ connected to a light spring of stiffness $k,$ with a speed $v_0.$ If the bullet gets embedded in the block then, the maximum compression in the spring is
$10\ m$ is the total mass of a cannon that includs all shell. Initial cannon is moving with velocity $10\ m$ is along a horizontal frictionless path. If cannon fires $'n$' shells of mass $m$ in the direction of motion of the cannon one by one with velocity $u$ with respect to ground. (neglect any friction force)
Two springs have their force constant as $k_1$ and $k_2 (k_1 > k_2)$. when they are stretched by the same force
$A$ ball of mass $m = 60gm$ is shot with speed $v_0 = 22m/s$ into the barrel of spring gun of mass $M = 240g$ initially at rest on $a$ frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. What fraction of initial kinetic energy of the ball is now stored in the spring?
$A$ ball of mass $m$ is attached to the lower end of light vertical spring of force constant $k$. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal (unstretched) length, comes to rest again after descending through a distance $x.$