Q.

Two identical spherically symmetric planets, each of mass M, are somehow held at rest with respect to each other. Each planet has radius R, and the distance between the centers of the planets is 4R. If a rocket is launched from the surface of one planet with speed v, what is the minimum speed v so that the rocket can reach the other planet?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

2GM3R

b

2GMR

c

3GM4R

d

GMR

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

detailed_solution_thumbnail

The gravitational force vanishes at the midway point between
the planets, so the rocket only needs to
have enough energy to get there. The initial and final gravitational potential energies are
Ui=GMmRGMm3R=4GMm3R an Uf=2GMm2R=GMmR

Thus, the initial kinetic energy needed is 
12mv2=UfUi=GMm3R
which implies  v=2GM3R
 

Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon