This lesson includes 24 additional questions and 220 additional question variations for subscribers.

# Lesson Worksheet: Newton’s Law of Universal Gravitation Mathematics

In this worksheet, we will practice applying Newton’s law of universal gravitation to find the gravitational force between two masses.

**Q3: **

A planet has a mass of kg and a radius of 5,723 km. Given that the mass of the Earth is kg, its radius is 6,340 km, and the acceleration due to gravity at its surface is 9.8 m/s^{2}, find the acceleration due to gravity at the surface of the other planet, approximating your answer to the nearest two decimal places.

**Q7: **

Consider a denser planet that has the same volume as our planet but is four times the mass of Earth. A book is dropped from a height of 5 meters to fall freely under the gravity of the planet. If the same book is dropped here on Earth from the same height, find the ratio between the velocity just before it reaches the ground here on Earth and the velocity just before it reaches the ground on the other planet.

- A
- B
- C
- D
- E

**Q10: **

An astronaut dropped an object from a height of 2,352 cm above the surface of a planet, and it reached the surface after 8 s. The mass of the planet is kg, while that of the Earth is kg, and the radius of the Earth is m. Given that the gravitational acceleration of the Earth is , find the radius of the other planet.

- A m
- B m
- C m
- D m