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Three identical point masses, each of mass $1 k g$ lie in the $x - y plane$ at points $(0, 0) (0, 0.2 m)$ and $(0.2 m, 0)$ respectively. The gravitational force on the mass at the origin is :-

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$1.67 \times 10^{- 11} (\hat{i} + \hat{j}) N$

$3.34 \times 10^{- 10} (\hat{i} + \hat{j}) N$

$1.67 \times 10^{- 9} (\hat{i} + \hat{j}) N$

$3.34 \times 10^{- 10} (\hat{i} - \hat{j}) N$

answer is C.

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Detailed Solution

$F_{1} = F_{2} = \frac{G (1) (1)}{{(0.2)}^{2}} = \frac{6.67 \times 10^{- 11}}{0.04} = 1.67 \times 10^{- 9}$

$\vec{F_{n e t}} = F_{1} (\hat{i}) + F_{2} (\hat{j}) = F (\hat{i} + \hat{j}) = 1.67 \times 10^{- 9} (\hat{i} + \hat{j}) N$

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