G L Mittal and TARUN MITTAL Solutions for Chapter: Work, Power and Energy, Exercise 2: NUMERICALS

Find the work done when a $25 \mathrm{kg}$ weight is carried to the vertical height of $2.0 \mathrm{m}$ from the ground by pushing it up an inclined plane making an angle of $30°$ with the ground. Take $\left(g=9.8{\mathrm{ms}}^{-2}\right)$

The power of a pump-motor is $2 \mathrm{kW}$. How much water (in $\mathrm{kg}$) per minute can it raise to a height of $10 \mathrm{metre}$. $\left(g=10 \mathrm{m}/{\sec }^2\right)$

A man pulls a roller by a force of  $20\mathrm{kgf}$  applied at $60°$ with the ground. If he pulls it a distance of $10 \mathrm{m}$ in $1\mathrm{minute}$, calculate the power dissipated. Take $g=10{\mathrm{ms}}^{-2}$.

An engine can pull $500\mathrm{metric}$ ton load up an inclined plane rising $1$ in $100$ with a speed of  $10{\mathrm{ms}}^{-1}$. The frictional force offered by the plane is $2000 \mathrm{N}$. What is the power of the engine?

Given: $1\mathrm{metric} \mathrm{ton}= {10}^3\mathrm{kg}$ and $g=9.8{\mathrm{ms}}^{-2}$.

An engine pulls a $1500 \mathrm{kg}$ car on a level road at a constant speed of  $5.0 {\mathrm{ms}}^{-1}$ against a frictional force of  $500 \mathrm{N}$. Calculate the power expended by the engine. What extra power has the engine to expend in order to maintain the same speed of the car up an inclined plane, given that the angle of inclination of the inclined plane is $\theta ={\sin }^{-1}\left(\frac{1}{10}\right)$.

A ball A of mass $2.4 \mathrm{kg}$ suffers an elastic head-on collision with another ball $B$ at rest. After collision, the ball $A$ continues to move in the same direction with the speed $\frac{1}{5}$ of the original speed with which the ball has started moving forward. Find the mass of the ball $B$.

A $0.1 \mathrm{kg}$ ball moving at a speed of $10 {\mathrm{ms}}^{-1}$ collides with an identical ball at rest. After the collision, the two balls move symmetrically each making an angle of  $30°$ with the original direction of motion of the moving ball. Find the new speed of each ball. Is the collision elastic?

A $10 \mathrm{kg}$ ball A moving at a speed of $8.0 \mathrm{m}/s$ collision with a $20 \mathrm{kg}$ ball $B$ initially at rest After collision the balls  $A$ and $B$ move along direction making angle of  $30°$ and $45°$ respectively with the initial direction of motion of  $A$. Find the final speed of $A$ and $B$.