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G = 6.67 x 10^{-11} Nm^{2}/kg^{2}

Imagine a planet started shrinking without any change in mass. Once the planet reached one-half its original diameter, the weight of objects on its surface would be

a. half their original weight.

b. the same weight as their original weight.

c. twice their original weight.

d. four times their original weight.

d. four times their original weight. (inverse square of separation)

1. A mass of 20.0 kg is located 4.0 m to the right of a mass of 30.0 kg.

a. What is the force on the 20.0 kg mass?

b. What is the force on the 30.0 kg mass?

2. At what point between the Earth and the Moon is the gravitational pull of the Earth equal in magnitude to that of the moon?

3. Find the altitude above the Earth's surface where Earth's **gravitational field strength** would be two-thirds of its value at the surface.

4. Four masses form the vertices of a 1 m X 1 m square as shown. What is the **gravitational force** on the 3 kg mass due to the other three masses?

5. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

6. The gravitational field intensity at the surface of a planet is 3.4N/kg. If a planet's mass is 7.2*10^{22} kg, what is its radius?

7. An object projected at 127 m/s upward from a small moon reaches a height of 5.08 km. If the radius of the moon is 1820 km, calculate its mass.

8. Estimate the surface **gravity** on a star that has five times the mass of our sun, and a radius of 10 km.

9. If the mass of Titan is 1.35*10^{23} kg and it's radius is 2570 km determine

a. the force at the surface on a 500 kg boulder.

b. the acceleration due to gravity.

10. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

11. What is the acceleration due to gravity at an altitude of 2*10^{6 }m above the earth\'s surface? Earth's mass is 5.98*10^{24 }kg and of Earth's radius is 6.37*10^{6} m .

12. A 492kg uniform solid sphere has a radius of .405m. Find the magnitude of the gravitational force (in N) exerted by the sphere on a 50.4g particle located 0.197m from the center of the sphere.

13. A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

Selected solutions are printed below.

For solutions to all the problems on this page click here.

1. F = Gm_{1}m_{2}/R^{2}

F = (6.67 x 10^{-11})(20.0 kg)(30.0 kg)/(4.0 m)^{2}

F = 2.50 x 10^{-11} N

a. 2.50 x 10^{-11} N [left]

b. 2.50 x 10^{-11} N [right]

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