Question

Two bodies a and b having masses 20kg and 40 kg are separated by 10 m. At what dist. From body a should another body c of mass 15kg be placed so that net gravitational force on body c is zero

Answer 1

Answer:

Mass of body a is Ma=20kg

Mass of body b is Mb=40kg

Mass of body cis Mc=15kg

Separation between a and b=10m

Let the body C be placed at a distance d fron the body A,

The gravitational force between A and C,

FAC=GMaMc/d^2=G*20*15/d^2=30G/d^2......1

the gravitational force between B and C is 

FBC=GMbMc/d^2=G*40*15/(10-d)^2=600G/(10-d)^2

For body C the gravttatinal force =0

hence Fac=Fbc

30G/d^2=600G/(10-d)^2

1/d^2=20/(10-d)^2

d^2=20(10-d)^2;

10-d=root of 20d

(√20+1)d=10

d=1.828m