The minimum energy required to launch a satellite of mass from the surface of Earth of mass and radius in a circular orbit at an altitude of from the surface of the Earth is [2024]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The minimum energy required to launch a satellite of mass $m$ from the surface of Earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ from the surface of the Earth is [2024]

1 $\frac{5 G m M}{6 R}$

2 $\frac{2 G m M}{3 R}$

3 $\frac{G m M}{2 R}$

4 $\frac{G m M}{3 R}$

Ans.
(1)

Energy of satellite on surface of earth,

$E_{i} = - \frac{G m M}{R}$

The energy at distance $(2 R + R = 3 R),$

$E_{f} = \frac{- G M m}{2 (3 R)} = \frac{- G M m}{6 R}$

Energy required to launch the satellite,

$E = E_{f} - E_{i} = \frac{- G M m}{6 R} - (\frac{- G M m}{R})$

$= \frac{5 G M m}{6 R}$

Want Us to Email you About Special Offers & Updates?