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In this lesson, we will learn how to solve problems for a particle moving away from or toward Earth's surface using Newton's law of universal gravitation.

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?

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 . 6 7 × 1 0 − 1 1 N⋅m^{2}/kg^{2}.

Q3:

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 . 1 6 4 × 1 0 2 4 kg, while that of the Earth is 5 . 9 7 × 1 0 2 4 kg, and the radius of the Earth is 6 . 3 4 × 1 0 6 m. Given that the gravitational acceleration of the Earth is 𝑔 = 9 . 8 / m s 2 , find the radius of the other planet.

Q4:

Given that a planet has a mass of 6 . 0 1 × 1 0 2 4 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 . 6 7 × 1 0 − 1 1 N⋅m^{2}/kg^{2}.

Q5:

Given that the gravitational force between two bodies of masses 4.6 kg and 2.9 kg was 3 . 2 × 1 0 − 1 0 N, find the distance between their centres. Take the universal gravitational constant 𝐺 = 6 . 6 7 × 1 0 ⋅ / − 1 1 2 2 N m k g .

Q6:

Given that the force of gravity acting between the sun and a planet is 4 . 3 7 × 1 0 2 1 N, where the mass of that planet is 2 . 9 × 1 0 2 4 kg, and that of the sun is 1 . 9 × 1 0 3 0 kg, find the distance between them. Take the universal gravitational constant 𝐺 = 6 . 6 7 × 1 0 ⋅ / − 1 1 2 2 N m k g .

Q7:

A satellite of mass 2 415 kg is orbiting the Earth 540 km above its surface. Given that the universal gravitational constant is 6 . 6 7 × 1 0 − 1 1 N⋅m^{2}/kg^{2} and the Earth’s mass and radius are 6 × 1 0 2 4 kg and 6 3 6 0 km, determine the gravitational force exerted by the Earth on the satellite.

Q8:

A satellite of mass 1.02 tonnes orbits the Earth at a constant height. If the mass of the Earth is 6 × 1 0 2 4 kg, its radius is 6 360 km, and the gravitational force between the Earth and the satellite is 6 . 6 × 1 0 3 N, find the height of the satellite’s orbit rounded to the nearest kilometre. Take the universal gravitational constant 𝐺 = 6 . 6 7 × 1 0 ⋅ / − 1 1 2 2 N m k g .

Q9:

Find the mass of a planet, given that the acceleration due to gravity at its surface is 6.003 m/s^{2}, its radius is 2 400 km, and the universal gravitational constant is 6 . 6 7 × 1 0 − 1 1 N⋅m^{2}/kg^{2}.

Q10:

If the mass of a planet is 4 . 0 8 × 1 0 2 4 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 . 6 7 × 1 0 − 1 1 N⋅m^{2}/kg^{2}.

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 . 3 4 × 1 0 6 m, calculate the radius of the other planet.

Q12:

Given that a planet’s mass and diameter are 4 and 8 times those of Earth respectively, calculate the ratio between the acceleration due to gravity on that planet and that on Earth.

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