__Question 8.21__:

__Solution__:Mass of each sphere,

*M*= 100 kg

Separation between the spheres,

*r*= 1m

X is the mid point between the spheres. Gravitational force at point X will be zero. This is because gravitational force exerted by each sphere will act in opposite directions.

Gravitational potential at point

*X:*

= -GM / (r/2) - GM / (r/2) = -4GM / r

= 4 X 6.67 X 10

^{-11}X 100 / 1

= -2.67 X 10

^{-8}J/kg

Any object placed at point X will be in equilibrium state, but the equilibrium is unstable. This is because any change in the position of the object will change the effective force in that direction.

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