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

In the solar system,which quantity is conserved?

$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

$A$ body of mass $m$ starts falling from a point $2R$ above the Earth's surface. What is its kinetic energy when it has fallen to a point $R$ above the Earth's surface? [$R$ = Radius of Earth,$M$ = Mass of Earth,$G$ = Gravitational Constant]

The escape velocity from a planet is $V_e$. $A$ tunnel is dug along the diameter of the planet and a small body is dropped into it. The speed of the body at the centre of the planet will be

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

Vedclass Test Series

Exam Paper Generator

Online Exam Module