Question

a body of mass 1 kg is placed at a distance of 2 m from another body of mass 10 kg. At what distance from the body of mass 1 kg, another body must be placed so that the net gravitational force acting on the body of mass 1 kg is zero

Answer 1

To answer this problem, we will use the formula for gravitational force:

F = G m1 m2 / r^2

Where,

G = gravitational constant (6.67 * 10^-11)

m = mass of a body

r = distance between two bodies

To have a net gravitational force equal to zero acting on body of mass 1 kg, then the forces of 1 kg and 10 kg bodies and 1 kg and 5 kg bodies should be equal.

F1 (1 kg and 10 kg) = F2 (1 kg and 5 kg)

Therefore,

(1 kg) (10 kg) / (2 m)^2 = (1 kg) (5 kg) / r2^2

Calculating for r2 (distance of another body 5 kg from body of mass 1 kg):

r2^2 = 2

r2 = 1.41 m (ANSWER)

Therefore another body of mass 5 kg should be placed 1.41 m from body of mass 1 kg to have a net gravitational force equal to zero.