Question

A satellite is orbiting the earth. Its speed is more at point B as compared to point A. Which of the following statements are true?

I. The gravitational force is greater at B than at A.
II. The speed is greater at B than at A.
III. The kinetic energy is greater at B than at A.
IV. The angular momentum is greater at B than at A.

• A. I only
• B. I and II only
• C. II only
• D. I, II and III only
• E. I, II, III, IV

Answer 1

The correct option is D I, II and III only

Since the speed is greater at point B, the kinetic energy $\frac{1}{2}m{v}^2$ is also greater at point B.

The gravitational force provides the centripetal acceleration to the satellite.

Thus $\frac{m{v}^2}{R}=\frac{GMm}{R^2}=F$

$⟹\frac{1}{2}m{v}^2\propto F$

Hence point B has more gravitational force.

From the above equation, $R\propto \frac{1}{v^2}$

The angular momentum of the satellite=$mvR\propto \frac{1}{v}$

Hence momentum is more at point A.