$A$ block of mass '$m$' (as shown in the figure) moving with kinetic energy $E$ compresses a spring through a distance $25\,cm$ when its speed is halved. The value of the spring constant of the used spring will be $nE\;N\,m^{-1}$ for $n=$

If mechanical work is done on an object,does its kinetic energy increase or decrease?

An open knife edge of mass $50 \ g$ is dropped from a height $2 \ m$ on a wooden floor. If the blade penetrates up to a depth of $10 \ cm$ into the wood,the average resistance offered by the wood to the knife edge is $....N$

$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

State the principle of conservation of mechanical energy for a conservative force.

The velocity at which the $6 \text{ kg}$ mass (shown in the figure) strikes the ground when it is released from a height of $6 \text{ m}$ above the ground is . . . . . . $\text{m/s}$. Assume the pulley is massless and the string is light and inextensible. (Take $g = 10 \text{ m/s}^2$)