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What is the distance between a $0.300 kg$ billiard ball and a $0.400 kg$ billiard ball if the magnitude of the gravitational force between them is $8.80 \times 10 ⁻¹¹ N$ ? Take $G = 6.6 \times 10 ⁻¹¹ Nm ² kg⁻² .$

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0.3 m

0.2 m

0.09 m

0.002 m

answer is A.

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Detailed Solution

The distance between a

0.300 kg

billiard ball and a

0.400 kg

billiard ball if the magnitude of the gravitational force between them is

8.80 \times 10 ⁻¹¹ N

0.3 m

.
Given,
Mass of first billiard ball,

m_{1} = 0.300 kg

Mass of another ball,

m_{2} = 0.400 kg

Force of gravitation between the balls,

F_{g} = 8.80 \times 10 ⁻¹¹ N

Now,
According to Newton’s law of gravitation,

F = \frac{Gm_{1} m_{2}}{r^{2}}

Where

F

r

G

m_{1}

and

m_{2}

are the gravitational force, a distance of separation of masses, gravitational force and mass of the object

1

and

2

respectively.
It can also be written as

r = \sqrt{\frac{G m_{1} m_{2}}{F}}

On substituting the values, we get

\Rightarrow r = \sqrt{\frac{(6.6 \times 10^{- 11}) (0.3) (0.4)}{8.80 \times 10^{- 11}}}

\Rightarrow r = 3 \times 0.1

\Rightarrow r = 0.3 m

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