Question

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

Answer 1

that is your answer tell me right or not.

Answer 2

given, m1 = 1kg, m2 = 2kg and m3 = 3kg
r = 1m

force exerted by 2kg mass on 1 kg , F = Gm1m2/r²

F = G × 1 × 2/(1)² = 2G

force exerted by 3kg on the 1kg, F' = Gm1m3/r²

F' = G × 1 × 3/1² = 3G

because masses are placed at the corner of an equilateral triangle, so angle between two sides are 60° .

force F directed along line joining the masses m1 and m2 and F' directed along line joining the masses m1 and m3 .
so, angle between F and F' = 60°

so, magnitude of resultant force ,$F_{net}=\sqrt{F^2+F'^2+2FF'cos60^{\circ}}$

$F_{net}=\sqrt{4G^2+9G^2+2(2G)(3G)\frac{1}{2}}$

$F_{net}=\sqrt{19G^2}=\sqrt{19}G$

hence, net force = √19G
here G is gravitational constant e.g., G = 6.67 × 10^-11 N