$A$ bullet when fired at a target with a velocity of $100\,m/s$ penetrates $1\,m$ into it. If the bullet is fired at a similar target with a thickness of $0.5\,m$,then it will emerge from it with a velocity of:

$A$ spherical ball of mass $2 \text{ kg}$ falls from a height of $10 \text{ m}$ and is brought to rest after penetrating $10 \text{ cm}$ into sand. The average force exerted by sand on the ball is . . . . . . $\text{N}$. (Take $g = 10 \text{ m/s}^2$)

Correct the following sentence: 'System cannot possess mechanical energy but possesses work.'

What can be said about the law of conservation of energy?

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 $g = 10 \ m/s^2$):

$A$ body of mass $2 \, kg$ is projected vertically upwards with a kinetic energy of $490 \, J$. At what height will its kinetic energy become half of its initial value? $(g = 9.8 \, m/s^2)$