Question

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy $\frac{{{E}_{0}}}{4}.$ Its potential energy is

• A. $\frac{{{E}_{0}}}{4}$
• B. $\frac{{{E}_{0}}}{2}$
• C. $\frac{{{E}_{0}}}{8}$
• D. ${{E}_{0}}$

Answer 1

Answer: (B)

$\frac{{{E}_{0}}}{2}$

Answer 2

As, mechanical energy $=-\frac{GMm}{2R}$ $\Rightarrow$ $\frac{{{E}_{0}}}{4}=-\frac{GMm}{2R}$ Kinetic energy, $K=\frac{GMm}{2R}$ using $E=KE+PE$ $\frac{{{E}_{0}}}{4}=\frac{GMm}{2R}+U$ or $U=\frac{{{E}_{0}}}{4}-\frac{GMm}{2R}=\frac{{{E}_{0}}}{4}-\left( -\frac{{{E}_{0}}}{4} \right)=\frac{{{E}_{0}}}{2}$