A small satellite revolves around a heavy planet in a circular orbit. At a point in its orbit an impulse acts suddenly and instantaneously increases its kinetic energy `K` times without change in its direction of motion. The ratio of maximum to the minimum distance from the planet is [Assume mass of satellite is negligible small compared to that of planet]

Options

A. `K/(K+2)`
B. `K`
C. `(K+2)/K`
D. `1/K`

Answer

B

Explanation

`-int_(P_(c))^(0)dp=4/3Grho_(r)^(2)int_(0)^(R)rdr` ltBrgt `P_(c)=4/3piGrho_(r)^(2)(R^(2))/2`
`P_(c)=(GM_(0)^(2))/(R_(0)^(4))xx(3/(2pi))`