A block of mass $5 \mathrm{kg}$ is sliding down a smooth inclined plane as shown. The spring arranged near the bottom of the inclined plane has a force constant $600 \mathrm{N}/\mathrm{m}$. Find the compression in the spring at the moment the velocity of the block is maximum?

A force $F=-\frac{K}{x^2}\left(x\ne 0\right)$ acts on a particle along the X-axis. Find the work done by the force in displacing the particle from $x=+a$ to $x=+2a$. Take $K$ as a positive constant.

A force $F$, acting on a particle varies with the position $x$ as shown in the graph. Find the work done by the force in displacing the particle from $x=-a$ to $x=+2a$.

From a height of $20 \mathrm{m}$ above a horizontal floor, a ball is thrown down with a speed of $20 \mathrm{m}/\mathrm{s}$. After striking the floor, the ball bounces to the same height from which it was thrown. Find the coefficient of restitution for the ball and the floor? $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

A ball falls from a height of $10 \mathrm{m}$ on a hard horizontal floor and repeatedly bounces. If the coefficient of restitution is $\frac{1}{\sqrt{2}}$, what is the total distance travelled by the ball before it ceases to rebound?

Work done by gravitational force in lifting a bucket out of a well by means of a rope tied to the bucket.

The sign of work done by a force on a body is important to understand. State carefully if the following quantity is positive or negative:

Work done by friction on a body sliding down an inclined plane.

The sign of work done by a force on a body is important to understand. State carefully if the following quantity is positive or negative:

Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.