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 midpoint 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?

Asked by Pragya Singh | 1 year ago | 151

Given:

Radius of spheres, R = 0.10 m

Distance between two spheres, r = 1.0 m

Mass of each sphere, M = 100 kg

From the above figure, ‘A’ is the mid-point and since each sphere will exert the gravitational force in the opposite direction. Therefore, the gravitational force at this point will be zero.

Gravitational potential at the midpoint (A) is;

U= \( \left [ \dfrac{-GM}{\dfrac{r}{2}}+\dfrac{-GM}{\dfrac{r}{2}} \right ]\)

U= \( \left [ \dfrac{-4GM}{r} \right ]\)

U= \( \left [ \dfrac{-4\times (6.67\times 10^{-11})\times (1000)}{1.0} \right ] \)

\( ⇒ U= -2.668 \times 10-7 J /kg\)

Therefore, the gravitational potential and force at the mid-point of the line connecting the centres of the two spheres is = -2.668 x 10^{-7} J /kg

The net force on an object, placed at the mid-point is zero. However, if the object is displaced even a little towards any of the two bodies it will not return to its equilibrium position. Thus, the body is in an unstable equilibrium.

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