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.

Q1:

Find the mass of a planet, given that the acceleration due to gravity at its surface is 6.003 m/s2, its radius is 2,400 km, and the universal gravitational constant is 6.67×10 N⋅m2/kg2.

  • A6.4×10 kg
  • B5.184×10 kg
  • C6.4×10 kg
  • D5.184×10 kg

Q2:

Two planets are separated by a distance of 3×10 km. The mass of the first is 9.9×10 metric tons, and that of the other is 10 metric tons. Given that the universal gravitational constant is 6.67×10 N⋅m2/kg2, find the force of gravity between them.

  • A2.201×10 N
  • B7.337×10 N
  • C7.337×10 N
  • D7.337×10 N

Q3:

A planet has a mass of 8.4×10 kg and a radius of 5,723 km. Given that the mass of the Earth is 5.97×10 kg, its radius is 6,340 km, and the acceleration due to gravity at its surface is 9.8 m/s2, find the acceleration due to gravity 𝑔 at the surface of the other planet, approximating your answer to the nearest two decimal places.

Q4:

A piece of iron is placed 23 cm away from a piece of nickel that has a mass of 46 kg. Given that the force of gravity between them is 2.9×10 N, determine the mass of the piece of iron. Take the universal gravitational constant 𝐺=6.67×10/Nmkg.

Q5:

Determine the gravitational force between two identical balls each of mass 3.01 kg, given that the distance between their centers is 15.05 cm, and the universal gravitational constant is 6.67×10 N⋅m2/kg2.

  • A2.668×10 N
  • B2.668×10 N
  • C4.015×10 N
  • D2.668×10 N

Q6:

Given that the gravitational force between two bodies of masses 4.6 kg and 2.9 kg was 3.2×10 N, find the distance between their centers. Take the universal gravitational constant 𝐺=6.67×10/Nmkg.

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.

  • A45
  • B41
  • C12
  • D14
  • E21

Q8:

Given that a planet’s mass and diameter are 3 and 6 times those of Earth respectively, calculate the ratio between the acceleration due to gravity on that planet and that on Earth.

  • A121
  • B12
  • C1081
  • D112
  • E1108

Q9:

A satellite of mass 2,415 kg is orbiting the Earth 540 km above its surface. Given that the universal gravitational constant is 6.67×10 N⋅m2/kg2 and the Earth’s mass and radius are 6×10 kg and 6,360 km, determine the gravitational force exerted by the Earth on the satellite.

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 7.164×10 kg, while that of the Earth is 5.97×10 kg, and the radius of the Earth is 6.34×10 m. Given that the gravitational acceleration of the Earth is 𝑔=9.8/ms, find the radius of the other planet.

  • A2.536×10 m
  • B2.536×10 m
  • C2.113×10 m
  • D2.113×10 m

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

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