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

A particle of mass $5 \mathrm{kg}$ is free to slide on a smooth ring of radius $r=20 \mathrm{cm}$ fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed the top point $O$ of the ring. Initially the particle is at rest at a point $A$ of the ring such that $\angle OCA=60°$, $C$ being the centre of the ring. The natural length of the spring is also equal to $r=20 \mathrm{cm}$. After the particle is released and slides down the ring the contact force between the particle & the ring becomes zero when it reaches the lowest position $B$. Determine the force constant of the spring.

A light string $ABCDE$ whose mid point is $C$ passes through smooth rings $B$ and $D$, which are fixed in a horizontal plane distance $2a$ apart. To each of the points $A,C$ and $E$ is attached a mass $m$. Initially $C$ is held at rest at $O$ (mid point $BD$) and is then set free. What is the distance $OC$ in meter when $C$ comes to instantaneous rest?

(Given $a=3\mathrm{m}$)

The potential energy of a particle of mass $1\mathrm{kg}$ free to move along $x$-axis is given by $U\left(x\right)=\left(\frac{x^2}{2}-x\right)$ joule. If total mechanical energy of the particle is $2\mathrm{J}$, If the maximum speed of the particle is $v$, then find the value of $v^2$.

For what minimum value of $m_1$ in $\mathrm{kg}$ for which the block of mass $m$ will just leave the contact with surface? (Given: $m=8\mathrm{kg}$)

A ball of mass $1 \mathrm{kg}$ is released from position, A inside a fixed wedge with a hemispherical cut of radius $0.5 \mathrm{m}$ as shown in the figure. If the force exerted by the vertical wall $OM$ on wedge, when the ball is in position $B$, is $F$ then find the value of $\frac{F}{\sqrt{3}}$ in $N$. (neglect friction everywhere) (Take $g=10 {\mathrm{ms}}^{-2}$)

A bead of mass $m$ is tied at one end of a spring of spring constant $\frac{mg}{R}$and unstretched length $\frac{R}{2}$ and other end to fixed point $O$. The smooth semicircular wire frame is fixed in vertical plane. Find the normal reaction between bead and wire just before it reaches the lowest point. (Given : $m=100 \mathrm{gm}; g=10 \mathrm{m} {\sec }^{-2}$)

A particle $P$ of mass $m$ is attached by a light inextensible string of length $2a$ to a fixed point $O$. When vertically below $O,P$ is given a horizontal velocity $u$ as shown figure (i) When open $OP$ becomes horizontal the string hits a small smooth nail, $Q$ distant a from $O$ and the particle continues to rotates about $Q$ as centre as shown figure (ii) The particle just describes complete circles about the nail. The value of $\frac{u^2}{ga}$ is

The system is released from rest when spring is at its natural length. Spring constant is $100 {\mathrm{Nm}}^{-1}$ and mass of each block is $10 \mathrm{kg}$. The velocity '$v$' of block $A$ as a function of position $x$ is given as $v^2=Ax-B{x}^2$. The value of $\frac{A}{B}$ is equal to.