Question

Two identical solid spheres are placed
at a separation. A point mass m is
moved from one sphere to the other as
shown
Then the potential energy of m will

Answer 1

The potential energy m will first increase, then it will decrease as the distance between two solid spheres decreases.

Explanation:

• Potential energy is stored energy i.e potential of any object to transmit energy to perform an activity.

• This gives rise to kinetic energy. A rubber band is the perfect example of this.

• This potential energy can be found out using the formula −GMm/(R−x)−Gm(M−m)/x−GM(M−m)/R.

Answer 2

F ∝ R^4.

Explanation:

Mass of each sphere  M1 ​= M2 ​= ρ(4/3​πR³ ) where ρ is the density and R is the radius.

According to Newton's law of  Gravitation, the gravitational force between the two spheres F = GM1​M2​​ / (2R)² where G is the Universal Gravitational Constant (6.672 x 10-11Nm2/kg2).

 F = gM1​M2​​ / (2R)²

    = g * ρ(4/3​πR³ ) * ρ(4/3​πR³ ) / 4R²

 F   = 4/9 π²gρ²R^4

We find that F ∝ R^4.