A satellite of mass m is revolving round the earth of mass M , radius R in a circular orbit of radius a = n R with velocity v 0 . A small particle is projected from the satellite in the forward dire

Question

A satellite of mass m is revolving round the earth of mass M , radius R in a circular orbit of radius a = n R with velocity v 0 ​ . A small particle is projected from the satellite in the forward direction with relative velocity v = ( 2 5 ​ ​ − 1 ) v 0 ​ . If the ratio of the maximum distance to the minimum distance of the projectile from the earth's centre is q p ​ in lowest terms, find p + q .

TestHub · Accepted Answer

For the circular orbit, v 0 2 ​ = a GM ​ . After projection, the particle speed is v = 2 5 ​ ​ v 0 ​ . E = 2 1 ​ m 4 5 ​ v 0 2 ​ − a GM m ​ = 8 5 ​ a GM m ​ − a GM m ​ = − 8 3 ​ a GM m ​ Using E = − 2 a or bi t ​ GM m ​ gives a or bi t ​ = 3 4 ​ a . r ma x ​ + r min ​ = 2 a or bi t ​ , r min ​ = a r min ​ r ma x ​ ​ = 3 5 ​ = q p ​ ⇒ p + q = 5 + 3 = 8

Physics - Gravitation Question with Solution | TestHub

Doubts & Discussion

JEE Main 2027 (Class 12+)