A mass of $20\, kg$ moving with a speed of $10\,m/s$ collides with another stationary mass of $5\,kg.$ As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be ............. $J$

A block having mass $m$ collides with an another stationary block having mass $2\,m$. The lighter block comes to rest after collision. If the velocity of first block is $v$, then the value of coefficient of restitution will must be

This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements. 
Statement $- 1$: A point particle of mass m moving with speed $u$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f$ $\left( {\frac{1}{2}m{v^2}} \right)$ then $ f = \left( {\frac{m}{{M + m}}} \right)$ 

Statement $-2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of $10 \,m/s$. Time taken by the two radius vectors connecting point of explosion to fragments to make $90^o $ is ............ $\mathrm{s}$

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

A body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2 \,m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is