Q123 / 160 · WBJEE 2015 · Physics

A satellite has kinetic energy $K$, potential energy $V$ and total energy $E .$ Which of the following statements is true?

  • Correct answer
    A
    $K=-V / 2$
  • B
    $K=V / 2$
  • C
    $E=K / 2$
  • D
    $E=-K / 2$

Solution

As we know that for the earth and satellite system Kinetic energy, $\quad K=\frac{G M m}{2 a}$ Potential energy, $V=-\frac{G M m}{a}$ and total energy, $E=-\frac{G M m}{2 a}$ where, $a=$ radius of the orbit of the satellite and $m=$ mass of the satellite On the basis of above three expressions for the energies, we have $K=\frac{G M m}{2 a}=-\left(-\frac{G M m}{2}\right)=-\frac{V}{2}$

Hence, the correct answer is option: 'A'.

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