Answer the following:
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet's velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why?
$(c)$ An artificial satellite orbiting the earth in a very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance,however small. Why then does its speed increase progressively as it comes closer and closer to the earth?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$,he walks the same distance pulling the rope behind him. The rope goes over a pulley,and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) The burning of the rocket's casing due to friction results in a reduction of the rocket's mass. According to the law of conservation of energy,the heat energy required for burning is obtained at the expense of the rocket's own energy (its mass-energy and kinetic energy).
$(b)$ Gravitational force is a conservative force. By definition,the work done by a conservative force over any closed path is zero. Since a complete orbit is a closed path,the net work done by the gravitational force on the comet is zero.
$(c)$ As the satellite moves closer to the earth,its potential energy decreases significantly due to the reduction in height. According to the conservation of energy,this loss in potential energy is converted into kinetic energy. Therefore,the speed of the satellite increases as it spirals inward,despite the small loss of total energy due to atmospheric drag.
$(d)$ In case $(i)$,the force applied by the man on the mass is upward (against gravity),while the displacement is horizontal. Since the angle $\theta = 90^{\circ}$,the work done $W = Fs \cos 90^{\circ} = 0$. In case $(ii)$,the man pulls the rope,lifting the mass vertically by $2\; m$. The force and displacement are in the same direction $(\theta = 0^{\circ})$,so $W = mgs = 15 \times 9.8 \times 2 = 294\; J$. Thus,more work is done in case $(ii)$.

Explore More

Similar Questions

Consider the following two statements: $[A]$ The linear momentum of a system is zero. $[B]$ The kinetic energy of the particles of the system is zero.

$A$ body of mass $m$ is dropped from a height of $h$. Simultaneously,another body of mass $2m$ is thrown vertically upward with such a velocity $v$ that they collide at a height $h/2$. If the collision is perfectly inelastic,the velocity at the time of collision with the ground will be:

Difficult
View Solution

Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$,moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite directions,collide head-on. After the collision,$A$ moves with a speed of $1\, m/s$ in the same direction. Which of the following statements is correct?

In a collinear collision,a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy,the magnitude of the relative velocity between the two particles,after collision,is:

Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies,$E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo