A body of mass m starts falling from a distan | vedclass

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

Question

(D) The total mechanical energy is conserved. Let $r_1$ be the initial distance from the center of the Earth and $r_2$ be the final distance from the

Vedclass · Accepted Answer

$\frac{1}{4} \frac{GMm}{R}$

Vedclass · Answer

(D) The total mechanical energy is conserved. Let $r_1$ be the initial distance from the center of the Earth and $r_2$ be the final distance from the center of the Earth.Initial distance from center: $r_1 = 3R + R = 4R$.Final distance from center: $r_2 = R + R = 2R$.Initial potential energy: $U_1 = -\frac{GMm}{r_1} = -\frac{GMm}{4R}$.Final potential energy: $U_2 = -\frac{GMm}{r_2} = -\frac{GMm}{2R}$.Since the body starts from rest,initial kinetic energy $K_1 = 0$.By the law of conservation of energy: $K_1 + U_1 = K_2 + U_2$.$0 + (-\frac{GMm}{4R}) = K_2 + (-\frac{GMm}{2R})$.$K_2 = \frac{GMm}{2R} - \frac{GMm}{4R} = \frac{GMm}{4R}$.

$A$ body of mass $m$ starts falling from a distance $3R$ above the Earth's surface. When it reaches a distance $R$ above the surface of the Earth (radius $R$,mass $M$),its kinetic energy is:

Similar Questions

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 of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (where $g$ is acceleration due to gravity at the surface of the earth).

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?

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

$A$ body is thrown from the surface of the earth with velocity $u \ m \ s^{-1}$. The maximum height in meters above the surface of the earth up to which it will reach is ($R=$ radius of the earth,$g=$ acceleration due to gravity).

Vedclass Test Series

Exam Paper Generator

Online Exam Module