Question

A satellite of mass 'm' is revolving in an orbit of
radius 'R around a planet of mass 'M. It lost some
energy against the work in air resistance and shift to an orbit of radius r by 2 The Lost energy is
(1) GmM/2R
(2) GMm/R

(3) GMm/4R

(4) 2GmM/R
correct answer is first option​

Answer 1

Answer:

Option (1) $\frac{GMm}{2R}$

Explanation:

The total energy of the satellite in the orbit of radius R

$E=-\frac{GMm}{2R}$

When the satellite shifts to the orbit of radius R/2, the total energy will be

$E'=-\frac{GMm}{2\times (R/2)}$

$\implies E'=-\frac{GMm}{R}$

The energy lost = Change in total energy

$W=E-E'$

$\implies W=-\frac{GMm}{2R}-(-\frac{GMm}{R})$

$\implies W=-\frac{GMm}{2R}+\frac{GMm}{R}$

$\implies W=\frac{GMm}{2R}$

Hope this helps.