Worksheet: Newton’s Law of Universal Gravitation

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

Q1:

If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?

  • A 1 5 N
  • B5 N
  • C 5 2 N
  • D 2 5 N

Q2:

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

  • A 4 . 0 1 5 × 1 0 N
  • B 2 . 6 6 8 × 1 0 N
  • C 2 . 6 6 8 × 1 0 N
  • D 2 . 6 6 8 × 1 0 N

Q3:

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.

Q4:

Given that the force of gravity acting between the sun and a planet is 4.37×10 N, where the mass of that planet is 2.9×10 kg, and that of the sun is 1.9×10 kg, find the distance between them. Take the universal gravitational constant 𝐺=6.67×10/Nmkg.

  • A 4 . 3 4 8 × 1 0 m
  • B 1 . 1 2 3 × 1 0 m
  • C 8 . 4 1 × 1 0 m
  • D 2 . 9 × 1 0 m

Q5:

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.

Q6:

A satellite of mass 1.02 metric tons orbits Earth at a constant height. If the mass of Earth is 6×10 kg, its radius is 6,360 km, and the gravitational force between Earth and the satellite is 6.6×10 N, find the height of the satellite’s orbit rounded to the nearest kilometer. Take the universal gravitational constant, 𝐺, to be 6.67×10 N⋅m2/kg2.

Q7:

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.

  • A 1 2 1
  • B 1 2
  • C 1 0 8 1
  • D 1 1 2
  • E 1 1 0 8

Q8:

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.

  • A 6 . 4 × 1 0 kg
  • B 5 . 1 8 4 × 1 0 kg
  • C 6 . 4 × 1 0 kg
  • D 5 . 1 8 4 × 1 0 kg

Q9:

If the mass of a planet is 4.08×10 kg, and its radius is 6,152 km, find the acceleration due to gravity at a point that is 500 km below the surface. Let the universal gravitational constant be 6.67×10 N⋅m2/kg2.

Q10:

Given that a planet has a mass of 6.01×10 kg and a radius of 6,014 km, find the acceleration due to gravity on its surface to the nearest two decimal places. Let the universal gravitational constant be 6.67×10 N⋅m2/kg2.

Q11:

A planet’s mass is 0.48 times the mass of Earth. The acceleration due to gravity at the surface of that planet is 0.12 times that on Earth’s surface. Given that the radius of Earth is 6.34×10 m, calculate the radius of the other planet.

  • A 1 . 2 6 8 × 1 0 m
  • B 2 . 5 3 6 × 1 0 m
  • C 1 . 2 6 8 × 1 0 m
  • D 2 . 5 3 6 × 1 0 m

Q12:

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.

  • A 2 . 5 3 6 × 1 0 m
  • B 2 . 5 3 6 × 1 0 m
  • C 2 . 1 1 3 × 1 0 m
  • D 2 . 1 1 3 × 1 0 m

Q13:

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.

Q14:

Determine the gravitational force between two balls of masses 5.9 kg and 10 kg, given that the distance between their centers is 10 cm and the universal gravitational constant is 6.67×10 N⋅m2/kg2.

  • A 3 . 9 3 5 × 1 0 N
  • B 6 . 6 7 × 1 0 N
  • C 3 . 9 3 5 × 1 0 N
  • D 3 . 9 3 5 × 1 0 N
  • E 2 . 3 2 2 × 1 0 N

Q15:

A satellite is held in orbit that is 310 km above the surface of the Earth by a gravitational force of magnitude 14,637 N. Given that the mass of the Earth is 6×10 kg, its radius is 6,360 km, and the universal gravitational constant is 6.67×10 N⋅m2/kg2, determine the mass of the satellite.

  • A 2 . 4 3 9 × 1 0 kg
  • B 1 . 3 3 9 × 1 0 kg
  • C16.27 kg
  • D 1 . 6 2 7 × 1 0 kg

Q16:

A space station weighs 353,278.1 N on the surface of the Earth. Given that the mass of the Earth is 5.98×10 kg, its radius is 6.37×10 kg, and the acceleration due to gravity at its surface is 𝑔=9.8/ms, find the force of gravity required to hold the space station in its orbit 335 km above the surface of the Earth. Round your answer to the nearest newton.

Q17:

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.

  • A 2 . 2 0 1 × 1 0 N
  • B 7 . 3 3 7 × 1 0 N
  • C 7 . 3 3 7 × 1 0 N
  • D 7 . 3 3 7 × 1 0 N

Q18:

A spaceship weighs 17,883.5 N on Earth, whereas, on another planet, its weight is 35,767 N. Given that Earth’s mass is 5.97×10 kg and its radius is 6.34×10 m, find the radius of the other planet if it has a mass of 2.985×10 kg.

  • A 3 . 1 7 × 1 0 m
  • B 6 . 3 4 × 1 0 m
  • C 6 . 3 4 × 1 0 m
  • D 3 . 1 7 × 1 0 m

Q19:

A rocket had a mass of 16.5 tons when it took off from the surface of the Earth. By the time it was 120 km above the ground, it had lost 16 of its mass as a result of burning its fuel. Find the weight of the rocket at this point, given that the mass of the Earth is 5.97×10 kg, its radius is 6,360 km, and the universal gravitational constant is 6.67×10 N⋅m2/kg2.

Q20:

When two masses are a distance 𝑑 apart, the gravitational force between them is 𝐹. If the distance between them changes so that they become 𝑑 apart, the gravitational force 𝐹 between them becomes 12𝐹. Find 𝑑𝑑.

  • A 2 1
  • B 1 2
  • C 2 1
  • D 1 2

Q21:

In a star system, there are two planets. The first has a mass of 1.2×10 kg, a radius of 4,000 km, and the acceleration due to gravity at its surface is 𝑔, where as the second planet has a mass of 6×10 kg, a radius of 8,000 km, and the acceleration due to gravity on its surface is 𝑔. Find 𝑔𝑔, given that the universal gravitational constant is 6.67×10 N⋅m2/kg2.

  • A 2 1
  • B 1 2
  • C 8 1
  • D 1 8

Q22:

If the radii of two planets are 𝑅=1,552km and 𝑅=6,208km, and the ratio between their gravitational accelerations 𝑔𝑔=12, find the ratio between their masses 𝑚𝑚.

  • A 1 1 6
  • B 1 6 4
  • C 1 3 2
  • D 1 8

Q23:

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.

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