Embibe Experts Solutions for Chapter: Work, Power & Energy, Exercise 1: Exercise 1

The force acting on the system is represented against distance $r$ as shown. The potential energy of the system will be best represented by. (At $x=0,$ potential energy $=0$) 

In the figure shown the potential energy $U$ of a particle is plotted against its position $x$ from origin. Then which of the following statement is correct. A particle at:

A block of mass $m$ slides along the horizontal track with kinetic friction $\mu .$ A man pulls the block through a light rope which makes an angle $\theta$ with the horizontal as shown in the figure. The tension in the light rope is $T$ as shown. The block moves with constant speed $v$. Power delivered by the man to the block is:

An engine pumps up $1000 \mathrm{kg}$ of coal from mine $100 \mathrm{m}$ deep in $0.5 \mathrm{s}.$ The pump is running with diesel and efficiency of the diesel engine is $25\%.$ Then its power consumption will be $\left(g\mathit{=}10 \mathrm{m} {\mathrm{s}}^{-2}\right):$

A self propelled vehicle of mass $m$ ,velocity $v$, whose engine delivers constant power $P$ has an acceleration $a=\frac{P}{mv}$ (assume that there is no friction). In order to increase its velocity from $v_{\mathit{1}}$ to $v_{\mathit{2}}$ the distance, it has to travel will be:

Water is flowing in a river at rate $2.0 \mathrm{m} {\mathrm{s}}^{-1}$. The river is $50 \mathrm{m}$ wide and has an average depth $5.0 \mathrm{m}$. The power from the river flow current is,

(density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$, Assume no velocity gradient with depth)

The kinetic energy $K$ of a particle moving along a circle of radius $r$ depends on the distance covered as $K\mathit{=}A{s}^2$ where $A$ is a constant. Find the force acting on the particle as a function of $s$.

The work done by the frictional force on a surface in drawing a circle of radius $r$ on the surface by a pencil of negligible mass with a normal pressing force $N$ (coefficient of friction ${\mu }_{\mathrm{k}}$ ) is :