An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational...

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An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?
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1/16W
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16W
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4W
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W
Select {responseValue}
1/4W

SnapAndSolve AI · Accepted Answer

To determine the gravitational force on the object when it is moved to a distance of \( 4R \) from the center of the planet, we can use the formula for gravitational force:
\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]
where
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) is the mass of the planet,
- \( m_2 \) is the mass of the object,
- \( r \) is the distance from the center of the planet to the object.
At the surface of the planet (distance = \( R \)), the weight \( W \) of the object is given by:
\[
W = \frac{G \cdot m_1 \cdot m_2}{R^2}
\]
When the object is moved to a distance of \( 4R \) from the center of the planet, the new gravitational force \( F' \) becomes:
\[
F' = \frac{G \cdot m_1 \cdot m_2}{(4R)^2} = \frac{G \cdot m_1 \cdot m_2}{16R^2}
\]
Now we relate \( F' \) to \( W \):
\[
F' = \frac{1}{16} \cdot \frac{G \cdot m_1 \cdot m_2}{R^2} = \frac{1}{16}W
\]
Thus, when the object is moved to a distance of \( 4R \) from the center of the planet, the gravitational force on the object will be:
1/16W

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An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational...

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