When a body is acted upon by a resultant force, then the work done by the resultant force is equal to

$A$ bullet of mass $20 \,g$ leaves a rifle at an initial speed $100 \,m/s$ and strikes a target at the same level with speed $50 \,m/s$. The amount of work done by the resistance of air will be ......... $J$.

Explain the conservation of mechanical energy using the example of a falling ball.

Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP = 3 \ m$ and $OQ = 4 \ m$. $A$ block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$,which is always parallel to the line $PQ$ (see the figure). Assuming no frictional losses,the kinetic energy of the block when it reaches $Q$ is $(n \times 10) \ J$. The value of $n$ is (take acceleration due to gravity $g = 10 \ m/s^2$):

The work-energy theorem is valid in the presence of:

The average force necessary to stop a bullet of mass $20\, g$ moving with a speed of $250\, m/s$,as it penetrates into the wood for a distance of $12\, cm$ is