$A$ particle which is experiencing a force,given by $\vec F = 3\hat i - 12\hat j$,undergoes a displacement of $\vec d = 4\hat i$. If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement,what is its kinetic energy (in $J$) at the end of the displacement?

$A$ bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistance of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $ms^{-1}$

$A$ small block slides down from rest at point $A$ on the surface of a smooth cylinder,as shown. At point $B$,the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by

$A$ ball of mass $20 \ kg$ is at rest on a hill of height $100 \ m$. It starts rolling down,reaches the ground,climbs another hill of height $30 \ m$,and finally rolls down to a horizontal platform at a height of $20 \ m$ from the ground. What will be its velocity at this point? (Assume $g = 10 \ m/s^2$)

$A$ bullet of mass $10 \ g$ is fired with a velocity of $800 \ m/s$. After passing through a mud wall of thickness $1 \ m$,its velocity decreases to $100 \ m/s$. Find the average resistive force exerted by the mud wall in $N$.

$A$ closed circular tube of average radius $15\,cm$,whose inner walls are rough,is kept in a vertical plane. $A$ block of mass $1\,kg$ just fits inside the tube. The speed of the block is $22\,m/s$ when it is introduced at the top of the tube. After completing five oscillations,the block stops at the bottom region of the tube. The work done by the tube on the block is $......J$. [Given $g=10\,m/s^2$]