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A mass of $40 kg$ is attracted by a mass of $25 kg$ placed at a distance of $2 m$ from it with a force of $1.67 \times 10^{- 8} N$ . The value of $G$ will be

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6.68 \times 10^{- 11} N m^{2} / {kg}^{2}

6.68 \times 10^{- 10} N m^{2} / {kg}^{2}

6.68 \times 10^{- 15} N m^{2} / {kg}^{2}

6.68 \times 10^{- 8} N m^{2} / {kg}^{2}

answer is A.

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Detailed Solution

The value of

G

will be

6.68 \times 10^{- 11} N m^{2} / {kg}^{2}

.
Given data:
Masses of the objects,

m_{1} m_{2} = 40 kg 25 kg

respectively.
Distance between the objects,

d = 2 m

.
Force between the objects,

F = 1.67 \times 10^{- 8} N

According to universal law of gravitation,

F = \frac{G m_{1} m_{2}}{d^{2}}

Where,

G =

Universal Gravitational Constant

1.67 \times 10^{- 8} = \frac{G \times 40 \times 25}{{(2)}^{2}}

\Rightarrow

G = \frac{4 \times 1.67 \times 10^{- 8}}{1000}

\Rightarrow

G = 6.68 \times 10^{- 11} N m^{2} / {kg}^{2}

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