When Royce was 10 years old, he had a mass of
30 kg. By the time he was 16 years old, his mass
increased to 60 kg. How much larger is the
gravitational force between Royce and Earth at
age 16 compared to age 10?

"Newton's law of universal gravitation states that gravitation force between two masses is proportional to the magnitude of their masses and inverse-squared of their distance".

Royce Scenario

At the age of 10 Royce's mass = 30kg

At the age of 16 Royce's mass = 60kg

From Newton's law of universal gravitation, an Increase in the mass of a body would amount to a corresponding increase in the gravitational force.

In the case of Royce, the mass double between the age of 10 and 16, so there would be an increase of the gravitation force by double.

Cricetus Cricetus · Answer 2 · 2021-11-28T18:05:20+01:00

The gravitational force at the age of 60 is doubled of the gravitational force at the age of 10. A complete solution is below.

Given:

At 10 years old,

Mass,

m = 30 kg

now,

→ [tex]Gravitational \ force (F_1) = \frac{GMm}{r^2}[/tex]

[tex]= mg[/tex]

or,

→ [tex]g = \frac{GM}{r^2}[/tex]

then,

Gravitational force = 30 g

Now,

At 16 years old,

Mass,

m = 60 kg

Now,

→ [tex]\frac{F_1}{F_2} = \frac{30}{60}[/tex]

[tex]=\frac{1}{2}[/tex]

[tex]F_2 = 2F_1[/tex]

Thus the above response is right.

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When Royce was 10 years old, he had a mass of 30 kg. By the time he was 16 years old, his mass increased to 60 kg. How much larger is the gravitational force between Royce and Earth at age 16 compared to age 10?

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When Royce was 10 years old, he had a mass of
30 kg. By the time he was 16 years old, his mass
increased to 60 kg. How much larger is the
gravitational force between Royce and Earth at
age 16 compared to age 10?