A 10 kg satellite completes one revolution around the earth at a height of 100 km in 108 minutes. The work done by the gravitational force of earth will be

The correct answer is Option 4: "Zero".

To understand why the work done by the gravitational force is zero, we can analyze the physics of circular orbital motion:
1. Nature of Gravitational Force: For a satellite orbiting the Earth, the gravitational force acts as the centripetal force. This force is directed radially inward, toward the center of the Earth.
2. Direction of Displacement: The instantaneous displacement of the satellite at any point along its circular orbit is tangential to the orbital path.
3. Angle between Force and Displacement: Since the force is radial (inward) and the displacement is tangential, the angle between the gravitational force vector ($\mathbf{F}$) and the displacement vector ($\mathbf{d}\mathbf{s}$) is exactly 90 degrees ($\theta ={90}^{\circ }$ or $\pi /2$ radians) at every point in the orbit.

The formula for the work done ($W$) by a force is given by the dot product of force and displacement:

$W=F·ds·cos\left(\theta \right)$

Substituting $\theta ={90}^{\circ }$ into the equation:

$W=F·ds·cos\left({90}^{\circ }\right)$

Since $cos\left({90}^{\circ }\right)=0$, the work done by the gravitational force on the satellite is:

$W=0\text{J}$

Therefore, no work is performed by the gravitational force during the orbital motion of the satellite.