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Q.

How does the force of gravitation between two objects change when the distance between them is reduced to half?

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a

2

times

b

4

times

c

1 / 2

times

d

1 / 4

times

answer is B.

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Detailed Solution

When the distance between the particles is reduced to half of its initial value, the gravitational force between them will become 4 times that initial value.
“Every particle in the universe is drawn to every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their distance from one another.” This statement is called Newton's universal law of gravitation. This can also be represented as,

F = G \frac{Mm}{r^{2}}

Where,

F

is the gravitational force acting between two particles of masses

M

and

m

separated by a distance

r

and

G

is the gravitational constant.
If the distance between the particles is reduced to half of its initial value, then the force of gravitation becomes

\Rightarrow F = \frac{GMm}{{(\frac{r}{2})}^{2}}

\Rightarrow F = 4 \frac{GMm}{r^{2}}

\Rightarrow F = 4 F

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How does the force of gravitation between two objects change when the distance between them is reduced to half?