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 ?
Given: The mass of each sphere is 100 kg , their radius is 0.10 m and they are placed 1.0 m 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 = − G M ( r 2 ) − G M ( r 2 ) = − 4 G M 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.
Given: The mass of each sphere is
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,
Where,
By substituting the given values in the above expression, we get
Thus, the gravitational potential at the mid point of the line joining the centers of the spheres is
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.
