Telangana Board Solutions for Chapter: Work, Energy and Power, Exercise 1: EXERCISES

A test tube of mass $10 \mathrm{grams}$ closed with a cork of mass $1\mathrm{gram}$ contains some ether. When the test tube is heated the cork flies out under the pressure of ether gas. The test tube is suspended horizontally by a weightless rigid bar of length $5 \mathrm{cm}$. What is the minimum velocity with which the cork should fly out the tube so that the test tube describing a full vertical circle about the point O? Neglect the mass of the ether.

Find the useful power used in pumping $3425 {\mathrm{m}}^3$ of water per hour from a well $8 \mathrm{m}$ deep to the surface, supposing $40\%$ of the horse power during pumping is wasted. What is the horse power of the engine?

A block of mass $5 \mathrm{kg}$ initially at rest at the origin is acted on by a force along the X-Positive direction represented by $F=\left(20+5x\right) \mathrm{N}$. Calculate the work done by the force during the displacement of the block from $x=0$ to $x=4 \mathrm{m}$.

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?