Question

A satellite of mass m is placed at a distance r from the centre of earth (mass M). The mechanical energy of the satellite is

• A. $-\frac{GMm}{r}$
• B. $\frac{GMm}{r}$
• C. $\frac{GMm}{2r}$
• D. $-\frac{GMm}{2r}$

Answer 1

The correct option is D $-\frac{GMm}{2r}$

Mechanical energy=K.E+U (kinetic energy + potential energy)

$U=-\frac{GmM}{r}$

$K.E$=$\frac{1}{2}m{v}^2$

$K.E=\frac{1}{2}\frac{GmM}{r}$

$M.E=K.E+U$

=$-\frac{GmM}{r}$+$\frac{1}{2}\frac{GmM}{r}$

$M.E=-\frac{GmM}{2r}$