What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?
5GmM/6R
2GmM/3R
GmM/2R
GmM/2R
A.
5GmM/6R
From conservation of energy,
Total energy at the planet = Total energy at the altitude
In its orbit the necessary centripetal force provided by gravitational force.
∴
Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
-4Gm/r
-6Gm/r
-9Gm/r
-9Gm/r
C.
-9Gm/r
The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius)
B.
The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g'and 'R'(radius of earth) are 10 m/s2 and 6400km respectively. The required energy for this work will be;
6.4 x1011 J
6.4 x108 J
6.4 x109 J
6.4 x109 J
D.
6.4 x109 J
Potential energy on the earth's surface is -mgR while in free space, it is zero. So, to free the spaceship minimum required energy is
E =mgR
= 103 x 10 x 6400 x 103 J
= 6.4 x 1010 J