Two point masses are separated by a distance r and exert a gravitational force F on each o… — JAMB UTME

Two point masses are separated by a distance $r$ and exert a gravitational force $F$ on each other. If the distance between them is doubled while keeping their masses constant, what is the new gravitational force between them?

$\frac{F}{4}$ Answer
B
$\frac{F}{2}$
C
$2F$
D
$4F$

Answer

The new gravitational force between the two masses is

\frac{F}{4}

Gravitational force obeys an inverse-square law with respect to distance (

F \propto \frac{1}{r^2}

). When separation distance is multiplied by 2, the force decreases by a factor of

2^2 = 4

, yielding

\frac{F}{4}

Step-by-Step Solution

Write down Newton's Law of Universal Gravitation

F = \frac{G m_1 m_2}{r^2}

Establish the mathematical relationship governing gravitational force and separation distance.

Substitute the new distance

r' = 2r

into the gravitational force equation

F' = \frac{G m_1 m_2}{(2r)^2} = \frac{G m_1 m_2}{4r^2}

Evaluate how doubling the separation distance affects the magnitude of the force.

Express the new force

F'

in terms of the initial force

F

F' = \frac{1}{4}\left(\frac{G m_1 m_2}{r^2}\right) = \frac{F}{4}

Relate the calculated force directly to the original force

F

Key Concept

Inverse-Square Law of Gravitation

Estimated Time:45s

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