Three spherical balls of masses 1 kg, 2kg and 3 kg are placed at the corners of an equilateral triangle of side 1 m. The magnitude of the gravitational force exerted by 2 kg and 3 kg masses on 1 kg mass.

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√19 G

19G

G/√17

√17 G

answer is C.

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Detailed Solution

$F_{1} = G \cdot \frac{1 \times 2}{1^{2}} = 2 G$
$F_{2} = G \cdot \frac{1 \times 3}{1^{2}} = 3 G$
$F = \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos 60^{0}}$
$= G \sqrt{2^{2} + 3^{2} + 2 \times 2 \times 3 \times \frac{1}{2}} = G \times \sqrt{19}$

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