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

A marble of mass $m$ and radius $b$ is placed in a hemispherical bowl of  radius $r$. the minimum velocity to be given to the marble so that it reaches the highest point is :

A particle of mass $4 \mathrm{m}$ which is at rest explodes into masses $\mathrm{m},\mathrm{m}$ and $2 \mathrm{m}$. Two of the fragments of masses m and $2 \mathrm{m}$ are found to move with equal speeds $v$ each in opposite directions. The total mechanical energy released in the process of explosion is:-

Two blocks $A\left(3\mathrm{kg}\right)$ and $B\left(2\mathrm{kg}\right)$ resting on a smooth horizontal surface is connected by a spring of stiffness $480 \mathrm{N} {\mathrm{m}}^{-1}$. Initially the spring is undeformed and a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ is imparted to $A$ along the line of the spring away from $B$. The maximum extension in meters of the spring during subsequent motion is:-

Two particles of mass $\mathrm{m}$, constrained to move along the circumference of a smooth circular hoop of equal mass $\mathrm{m}$, are initially located at opposite ends of a diameter and given equal velocities $v_0$ shown in the figure. The entire arrangement is located in gravity free space. Their velocity just before collision is:-

A uniform rope of linear mass density $\lambda$ and length $l$ is coiled on a smooth horizontal surface. One end is pulled up with constant velocity $v$. Then the average power applied by the external agent in pulling the entire rope just off the ground is:-

The weight of a person is $60\mathrm{kg}$. If he gets $10$ calories of heat through food and the efficiency of his body is $28\%$, then upto what height he can climb? Take $g=10{\mathrm{ms}}^{-2}$

Hailstone at $0°\mathrm{C}$ falls from a height of $1 \mathrm{km}$ on an insulating surface converting the whole of its kinetic energy into heat. What part of it will melt: $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}, L_{ice}=330\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1}\right]$

Potential energy and kinetic energy of a two particle system are shown by $\mathrm{KE}$ and $\mathrm{PE}$. respectively in figure. This system is bound at :