$A$ $1.0\, kg$ block collides with a horizontal weightless spring of force constant $2.75\, N/m$ as shown in the figure. The block compresses the spring $4.0\, m$ from the rest position. If the coefficient of kinetic friction between the block and the horizontal surface is $0.25$,the speed of the block at the instant of collision is ................. $m/s$.

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9 \ m/s$ and makes an elastic collision with it. Thereafter,$B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is $.... \ m/s$.

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.5 \; m$,what is the speed (in $m/s$) with which the bob arrives at the lowermost point,given that it dissipated $5 \%$ of its initial energy against air resistance?

Two bodies have kinetic energies in the ratio $16: 9$. If they have the same linear momentum,the ratio of their masses respectively is

In an inelastic collision,

Two persons $A$ and $B$ are throwing a ball of mass $200 \ g$ at a wall as shown in the figure. The balls strike the wall perpendicularly at the same point at a height of $2 \ m$ from the ground. The balls strike the wall elastically at the same time and return back to $A$ and $B$ at the same time. They repeat this process. What is the average force exerted on the wall (in $N$)? (Take $g = 10 \ m/s^2$)