10 minutes maximum! Can you do it in 5?

1. Gravitational fields have 'equipotential surfaces'. These are always..

• A. equally spaced.
• B. perpendicular to gravitational field lines.
• C. circular.
• D. parallel to the surface of any astronomical body.

2. Which of these diagrams best shows the shape of the equipotential surfaces around the two stars?

3. Which of these formulas gives the energy E required to move both stars to 'infinite separation'?

• A. $E = -{2GM \over r} $
• B. $E = -{GM^2 \over r} $
• C. $E = {2GM \over r} $
• D. $E = {GM^2 \over r} $

4&5. Two small objects of mass m and 2m are located at distances r and 2r from a much larger planet of mass M as shown.

4. The ratio $gravitational~potential~at~m \over gravitational~potential~at~2m $ due to the planet is:

• A. 2
• B. ½
• C. 4
• D. ¼

5. The graph below shows how the gravitational potential (V) varies with distance (r) from the planet.

What is shown by the gradient of the line at any point?

• A. Gravitational field strength
• B. Force of gravity
• C. Energy per unit mass required to move an object from that point to infinity
• D. Total energy required to move an object from that point to infinity

6. A space ship is accelerated along the Moon's surface and then projected into space. It requires an escape velocity of v.

To reach deep space from a different moon with no atmosphere, the same mass but four times the radius will require a velocity of:

• A. ¼v
• B. ½v
• C. 2v
• D. 4v

7. A body of mass m is in orbit at a distance r around a planet of mass M.
The kinetic energy E_k of the body is:

8. This means that if a 10 kg rock is lifted from the Moon's surface into space:

• A. 28 MJ of energy is released.
• B. 28 MJ of energy is required.
• C. 0.28 MJ of energy is released.
• D. 0.28 MJ of energy is required.

9. To calculate the gravitational energy increase for this rock over a small height increase Δr, the formula required is:

10. A satellite in orbit around the Earth experiences a small viscous drag force due to the upper atmosphere. What is the immediate effect of this on the radius of orbit and resulting speed of the satellite?