The energy required to take a body from the s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the earth is given by $U = -\frac{GMm}{r}$.At the su

Vedclass · Accepted Answer

$\frac{4 W}{3}$

Vedclass · Answer

(D) The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the earth is given by $U = -\frac{GMm}{r}$.At the surface of the earth,$r = R$,so $U_i = -\frac{GMm}{R}$.For a height $h = R$,the distance from the center is $r = R + R = 2R$. The potential energy is $U_f = -\frac{GMm}{2R}$.The energy required $W$ is the change in potential energy:$W = U_f - U_i = -\frac{GMm}{2R} - (-\frac{GMm}{R}) = \frac{GMm}{2R}$.For a height $h = 2R$,the distance from the center is $r = R + 2R = 3R$. The potential energy is $U_f' = -\frac{GMm}{3R}$.The energy required $W'$ is:$W' = U_f' - U_i = -\frac{GMm}{3R} - (-\frac{GMm}{R}) = \frac{GMm}{R} - \frac{GMm}{3R} = \frac{2GMm}{3R}$.Since $W = \frac{GMm}{2R}$,we have $\frac{GMm}{R} = 2W$.Substituting this into the expression for $W'$:$W' = \frac{2}{3} 	imes (2W) = \frac{4W}{3}$.

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth is:

Similar Questions

$A$ rocket is fired vertically upwards from the surface of the Earth with a velocity $V$. If $R$ is the radius of the Earth,what is the maximum height attained by the rocket?

An object of mass $m$ is raised from the surface of the earth to a height equal to the radius of the earth,that is,taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy?

An object is propelled vertically to a maximum height of $4 R$ from the surface of a planet of radius $R$ and mass $M$. The speed of the object when it returns to the surface of the planet is

Assuming that the gravitational potential energy of an object at infinity is zero,the change in potential energy (final - initial) of an object of mass $m$,when moved to a height $h$ from the surface of the Earth (of radius $R$),is given by:

$A$ body is projected vertically upwards with a speed of $\sqrt{\frac{G M}{R}}$ ($M$ is the mass and $R$ is the radius of the Earth). The body will attain a maximum height of .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module