Question

Total kinetic energy of a satellite at height \( h \) is \( k \). Then total energy of the satellite is

• A. \( -k \)
• B. \( -2k \)
• C. \( k \)
• D. \( -3k \)

Hint:

For a satellite in orbit, the total energy is always negative and is half the magnitude of the kinetic energy, but with the opposite sign.

Answer 1

The Correct Option is B

The total energy of a satellite in orbit is the sum of its kinetic energy and gravitational potential energy. The total energy \( E \) of the satellite is given by: \[ E = K + U \] where: - \( K \) is the kinetic energy of the satellite, - \( U \) is the potential energy. For a satellite at height \( h \), the total energy is negative and is related to the kinetic energy by: \[ E = - \frac{K}{2} \] Thus, if the kinetic energy at height \( h \) is \( k \), then the total energy is: \[ E = - \frac{k}{2} = -2k \] Therefore, the correct answer is \( -2k \).