Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.$ of block $A$ to the $K.E.$ of block $B$ is:

$A$ bullet of mass $50 \, g$ is fired from a $5 \, kg$ gun with a velocity of $1 \, km/s$. The speed of recoil of the gun is .......... $m/s$.

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space at first,then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest,the other piece of spacecraft will have a velocity

$A$ ball of mass $m$ strikes the inclined face of the wedge of mass $M$ normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before the collision. The conservation of momentum is applicable for the event of collision for:
$(i)$ $m$ as system,along $Y'$
$(ii)$ $M$ as system,along $Y'$
$(iii)$ $(M + m)$ as system,along $X$
$(iv)$ $(M + m)$ as system,along $Y$
Which of the following is correct?

$A$ ball of mass $10 \, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $X$-axis,hits another ball of mass $20 \, kg$ which is at rest. After the collision,the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along the $Y$-axis at a speed of $10 \, m/s$. The second piece starts moving at a speed of $20 \, m/s$ at an angle $\theta$ (in degrees) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$ to the nearest integer is:

When two balls at the same temperature collide,which of the following quantities is conserved?