Question

If the radius of the Earth were doubled (but its mass stayed the same), the weight of an object near the Earth's surface would...?

be halved.

quadruple.

be quartered.

double.

not change.

Answer 1

If the radius of the Earth were doubled (but its mass stayed the same), the weight of an object near the Earth's surface would be quartered.

This relationship is described by the law of universal gravitation, which states that the gravitational force
`(\(F\))` between two objects is directly proportional to the product of their masses
`(\(m_1\)` and
`\(m_2\)`) and inversely proportional to the square of the distance
`(\(r\))` between their centers:

`\[F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}}\]`

In this scenario, when the radius of the Earth is doubled
`(\(2r\))`, the distance
`(\(r\))` between an object near the Earth's surface and the center of the Earth becomes four times greater because it's twice as far from the center. When you square the denominator in the equation
`(\(r^2\))`, the effect is that the gravitational force becomes
`\((1)/(4)\)` of its original value. Therefore, the weight of the object would be quartered if the radius of the Earth were doubled.