Question

A satellite of mass 500 kg is in an orbit around the earth at a distance of \( 6.67 \times 10^6 \, m \) from the center of the Earth. The speed of the satellite is:

• A. 17.75 km/s
• B. 27.27 km/s
• C. 7.75 km/s
• D. 30.25 km/s

Hint:

The speed of a satellite in orbit around the Earth can be calculated using the formula \( v = \sqrt{\frac{GM}{r}} \), where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the center of the Earth.

Answer 1

The Correct Option is C

The speed of the satellite is given by the formula: \[ v = \sqrt{\frac{GM}{r}} \] Substituting the given values: \[ v = \sqrt{\frac{(6.67 \times 10^{-11}) \cdot (6 \times 10^{24})}{6.67 \times 10^6}} = 7.75 \, \text{km/s} \] Hence, the speed of the satellite is \( 7.75 \, \text{km/s} \).