JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Gravitation

A satellite of

1 0^{3} kg

mass is revolving in circular orbit of radius 2 R . If

\frac{1 0 ^{4} R}{6} J

energy is supplied to the satellite, it would revolve in a new circular orbit of radius :
(use

g = 10 m / s^{2}, R =

radius of earth)

(A)2.5 R
(B)3 R
(C)4 R
(D)6 R✓ Correct

Answer: (D)

Solution

Total mechanical energy of a satellite in a circular orbit of radius

r

E = - \frac{GM m}{2 r}

.

At

r = 2 R

E_{i} = - \frac{GM m}{4 R}

. Using

GM = g R^{2} = 10 R^{2}

and

m = 1 0^{3}

kg:

E_{i} = - \frac{( 10 R ^{2} ) ( 1 0 ^{3} )}{4 R} = - 2500 R J

Adding energy

Δ E = \frac{1 0 ^{4} R}{6} \approx 1666.7 R

E_{f} = - 2500 R + 1666.7 R = - 833.3 R J

Setting

E_{f} = - \frac{GM m}{2 r ^{'}}

\frac{( 10 R ^{2} ) ( 1 0 ^{3} )}{2 r ^{'}} = 833.3 R ⟹ r^{'} = 6 R

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · 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 →