Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 3: Exercise - 3

The upper half of an inclined plane with inclination $\varphi$ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by:

The work done on a particle of mass $m$ by a force, $\overrightarrow{F}=K\left[\frac{x}{{\left(x^2+y^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\hat{\mathrm{i}}+\frac{y}{{\left(x^2+y^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\hat{\mathrm{j}}\right]$, ($K$ being a constant of appropriate dimensions) when the particle is taken from the point $\left(a,0\right)$ to the point $\left(0,a\right)$ along a circular path of radius $a$ about the origin in the $x-y$ plane is,

A particle of mass $m=0.2 \mathrm{kg}$ is moving in one dimension under a force that delivers constant power $0.5 \mathrm{W}$ to the particle. If the initial speed of the particle is zero, find its speed after $5 \mathrm{s}$.

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$ -axis. Its kinetic energy $K$ changes with time as $\frac{dK}{dt}=\gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A ball of mass $0.2 \mathrm{kg}$ is thrown vertically upward by applying a force by hand. If the hand moves $0.2 \mathrm{m}$ while applying the force and the ball goes up to $2 \mathrm{m}$ height further, find the magnitude of the force. Consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

An athlete in the Olympic Games covers a distance of $100 \mathrm{m}$ in $10 \mathrm{s}$. His kinetic energy can be estimated to be in the range

When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2$ where a and b are constants. The work done in stretching the un stretched rubber-band by $L$ is

A time dependent force $\mathrm{F}=6\mathrm{t}$ acts on a particle of mass $1 \mathrm{kg}$. If the particle starts from rest, the work done by the force during the first $1 \mathrm{s}$ will be: