JEE Main · 2004 · 24 Apr 2004 · Offline · Gravitation

WhatsApp Email

g

is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass

m

raised from the surface of the earth to a height equal to the radius

R

of the earth is

(A)2 mgR
(B) $\frac{1}{2} mgR$ ✓ Correct
(C) $\frac{1}{4} mgR$
(D)mgR

Answer: (B)

Solution

At the surface the gravitational potential energy is

- \frac{GM m}{R}

, and at a height equal to one Earth radius, a distance

2 R

from the centre, it is

- \frac{GM m}{2 R}

. The gain is

- \frac{GM m}{2 R} - (- \frac{GM m}{R}) = \frac{GM m}{2 R}

. Since

g = \frac{GM}{R ^{2}}

gives

GM = g R^{2}

, this increase works out to

\frac{g R ^{2} m}{2 R} = \frac{1}{2} m g R

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

Practise more: all JEE Main PYQs on Gravitation →

More JEE Main questions on Gravitation

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.
JEE Main 2026View solution →
Net gravitational force at the centre of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio …
JEE Main 2026View solution →
Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …
JEE Main 2026View solution →
Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …
JEE Main 2026View solution →
Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 1 0^{6} J$ of energy. The value of $α$ is ______.
(Take …
JEE Main 2026View solution →
If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and $g = 9.8 m / s^{2}$ )
JEE Main 2026View solution →