To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is ) g = acceleration due to gravity on the surface of earth:

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.
To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_{E}$ ) g = acceleration due to gravity on the surface of earth: [2024]

1 $m g R_{E}$

2 $1 / 2 m g R_{E}$

3 $4 m g R_{E}$

4 $2 m g R_{E}$

Ans.
(1)

Escape speed $v_{e} = \sqrt{\frac{2 G M}{R_{E}}}$

Escape kinetic energy $K_{e} = \frac{1}{2} m v_{e}^{2}$

$K_{e} = \frac{1}{2} m {(\sqrt{\frac{2 G M}{R_{E}}})}^{2} = \frac{G M m}{R_{E}}$

Also, $G M = g R_{E}^{2} \Rightarrow K_{e} = \frac{(g R_{E}^{2}) m}{R_{E}} = m g R_{E}$

Want Us to Email you About Special Offers & Updates?