A body of mass m is taken from the earth's su | vedclass

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

Question

(A) The gravitational potential energy at a distance $r$ from the center of the earth is given by $U = -\frac{GMm}{r}$.At the surface of the earth,the

Vedclass · Accepted Answer

$\frac{2}{3}mgR$

Vedclass · Answer

(A) The gravitational potential energy at a distance $r$ from the center of the earth is given by $U = -\frac{GMm}{r}$.At the surface of the earth,the distance from the center is $r_i = R$.Therefore,the initial potential energy is $U_i = -\frac{GMm}{R}$.At a height $h = 2R$ from the surface,the distance from the center is $r_f = R + h = R + 2R = 3R$.Therefore,the final potential energy is $U_f = -\frac{GMm}{3R}$.The change in potential energy is $\Delta U = U_f - U_i$.$\Delta U = -\frac{GMm}{3R} - (-\frac{GMm}{R}) = \frac{GMm}{R}(1 - \frac{1}{3}) = \frac{2}{3}\frac{GMm}{R}$.Since the acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,we have $GM = gR^2$.Substituting this,$\Delta U = \frac{2}{3} \frac{(gR^2)m}{R} = \frac{2}{3}mgR$.

$A$ body of mass $m$ is taken from the earth's surface to a height equal to twice the radius $(R)$ of the earth. The change in potential energy of the body will be

Similar Questions

The change in the gravitational potential energy when a body of mass $m$ is raised to a height $h = nR$ above the surface of the Earth is (where $R$ is the radius of the Earth).

$A$ body starts from rest from a point at a distance $R_0$ from the centre of the Earth. The velocity acquired by the body when it reaches the surface of the Earth will be ($R$ represents the radius of the Earth).

$A$ body of mass $m$ is placed on the earth's surface. It is taken from the earth's surface to a height $h = 3R$ ($R$ is the radius of the earth). The change in gravitational potential energy of the body is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module