$A$ $2 \ kg$ block slides on a horizontal surface at a speed of $4 \ m/s$ and strikes an uncompressed spring. The kinetic friction force is $15 \ N$ and the spring constant is $10,000 \ N/m$. By how many $cm$ will the spring be compressed?

Statement $-1$: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement $-2$: Principle of conservation of momentum holds true for all kinds of collisions.

$A$ bullet of mass $0.01 \,kg$ travelling at a speed of $500 \,ms^{-1}$ strikes a block of mass $2 \,kg$ which is suspended by a string of length $5 \,m$. The centre of gravity of the block is found to rise a vertical distance of $0.1 \,m$. What is the speed of the bullet after it emerges from the block (in $\,ms^{-1}$)?

In a collinear collision,a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy,the magnitude of the relative velocity between the two particles,after collision,is:

$A$ block of mass $m(=0.1 \ kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force $F$ in the vertically downward direction. The linear momentum of the block increases by $2 \ kg \ m/s$ in $1 \ s$ after the block starts from rest. Then, (given $g=10 \ m/s^2$):

Which of the following statements is true?