Answer:
Given,
A 5 kg mass is at the origin. A 7 kg mass is located at x = 0.6 m and a 4 kg mass is at x = 0.9 m.
To find,
the net gravitational force on the 5 kg mass.
we know, from Newton's gravitational law, two massive bodies attract each other by a force , F = Gm₁m₂/r²
so, 7 kg mass attracts 5kg mass by the force, F₁ = G(7kg)(5kg)/(0.6)²
= 35G/0.36 = 97.22G
similarly, 4kg mass attracts 5kg mass by the force, F₂ = G(4kg)(5kg)/(0.9)²
= 20G/0.81 = 24.69G
net gravitational force = F₁ + F₂
= 97.22G + 24.69G
= 121.91G
we know, G = 6.67 × 10¯¹¹ Nm²/Kg²
F = 121.91 × 6.67 × 10¯¹¹
= 813.1397 × 10¯¹¹ N
= 8.131397 × 10^-9 N ≈ 8.13 × 10^-9 N
Therefore net gravitational force acting on mass 5kg is 8.13 × 10^-9 N