Question

A missile is launched with a velocity less than the escape velocity. Sum of its kinetic energy and potential energy is :

• A. Positive
• B. Negative
• C. May be negative or positive depending upon its initial velocity
• D. Zero

Answer 1

The correct option is B Negative

Suppose the mass of missile is m and mass and send to earth in circular orbit " r " Earth is ' M ' and radius ' R ' ,, so kinetic energy of missile is

Hence ,, the Total energy ( Et ) = Ek +Ep

Et = $\frac{1}{2}\times \frac{GMm}{r}+(-\frac{GMm}{r})$

Total Energy ( Et ) = - $\frac{GMm}{2r}$

Hence ,, total energy = -ve .

=> -ve sign here shows that missile is bounded under gravitational force of earth.