Answer to Question #8959 in Mechanics | Relativity for Rajat

Question

A body A of mass 1kg is placed at a distance of 2m from another of mass 10kg.At what distance from A another body of mass 5kg must be placed so that the net gravitational force on A is zero.

Answer 1

A body A of mass 1kg is placed at a distance of 2m from another of mass 10kg. At what distance from A another body of mass 5kg must be placed so that the net gravitational force on A is zero.

C(Mc=5kg)--------(Lac=?m)----------A(1kg)-----(Lab=2m)------B(Mb=10kg)

According to the Newton's gravity law:

Fab = G·Ma·Mb/Lab² = G·1·10/2² = 5G/2 N,

Fac = G·Ma·Mc/Lac² = G·1·5/Lac² = 5G/Lac² N.

Fab = Fac ==> 5G/Lac² = 5G/2 ==> Lac² = 2 ==> Lac = √2m.