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
${\left( {\frac{{{m^2}v_0^2}}{{(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{Mmv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{Mv_0^2}}{{2(M + m)k}}} \right)^{1/2}}$
${\left( {\frac{{m{v^2}}}{{(M + m)k}}} \right)^{1/2}}$
Two bodies having same mass $40\, kg$ are moving in opposite directions, one with a velocity of $10$$m/s$ and the other with $7\,m/s.$ If they collide and move as one body, the velocity of the combination is ........ $m/s$
Two massless string of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25 \,kg$ and $0.5 \,kg$ are attached to the string. The ball $A$ is released from rest at $a$ height $0.45\, m$ as shown in the figure. The collision between two balls is completely elastic. Immediately after the collision, the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is
A ball falling freely from a height of $4.9\,m,$ hits a horizontal surface. If $e = \frac {3}{4}$ , then the ball will hit the surface, second time after .............. $\mathrm{s}$
A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 N m ^{-1}$ and the mass of the block is $2.0 kg$. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass $1.0 kg$ moving with a speed of $2.0 m s ^{-1}$ collides elastically with the first block. The collision is such that the $2.0 kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is. . . . . .
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be