A300-kg object and a 600-kg object are separated by 4.60 m.

(a) find the magnitude of the net gravitational force exerted by these objects on a 35.0-kg object placed midway between them. n
(b) at what position (other than an infinitely remote one) can the 35.0-kg object be placed so as to experience a net force of zero from the other two objects

2.69 m

Explanation:

M = Mass in the middle = 35 kg

= 600 kg

= 300 kg

r = Distance

The net force between the objects would be

The magnitude of the net gravitational force exerted by these objects is

Now,

Solving the above equation we get

So, the distance at which the force will ben zero is 2.69 m

Explanation:

m1 = 300 kg

m2 = 600 kg

d = 4.6 m

(a) m = 35 kg

Let the force between m1 and m is F1. Use the Newton's gravitation law

F1 = 1.324 x 10^-7 N (towards m1, i.e., leftwards)

Let the force between m2 and m is F2. Use the Newton's gravitation law

F1 = 2.65 x 10^-7 N (towards m2, i.e., rightwards)

Net force on m is

F = F2 - F1

F = (2.65 - 1.324) x 10^-7

F = 1.33 x 10^-7 N towards right

(b) Let it is placed at a distance r from m1 so that the net force is zero.

1.414 r = 4.6 - r

2.4 r = 4.6

r = 1.92 m

Thus, the net force on 35 kg is zero at a distance of 1.92 m from 300 kg.

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