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Question

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable ?

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Solution

Given: The mass of each sphere is 100kg, their radius is 0.10m and they are placed 1.0m apart.

The situation is represented by the figure below.



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

Gravitational potential at point X is given as,

P= GM ( r 2 ) GM ( r 2 ) =4 GM r

Where, M is the mass of each sphere and r is the distance between each sphere.

By substituting the given values in the above expression, we get

P= 4×6.67× 10 11 ×100 1 =2.67× 10 8 Jkg 1

Thus, the gravitational potential at the mid point of the line joining the centers of the spheres is 2.67× 10 8 Jkg 1 .

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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