Question

An artificial satellite revolves around the earth in a circular orbit with a speed $ v $ . If m is the mass of the satellite, its total energy is

• A. $ \frac{1}{2}mv^{2}$
• B. $ -\frac{1}{2}mv^{2}$
• C. $ -mv^{2}$
• D. $ \frac{3}{2}mv^{2}$

Answer 1

The Correct Option is B

Kinetic energy of satellite, $KE=\frac{1}{2} m v^{2}$ where $v=\sqrt{\frac{G M}{r}}$ Potential energy of satellite, $PE =\frac{-G M m}{r}=-m v^{2}$ $\therefore$ Total energy $=KE+PE$ $=\frac{1}{2} m v^{2}-m v^{2}=-\frac{1}{2} m v^{2}$