Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.250 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide? (Hint: Consider conservation of energy and of linear momentum.) m/s (lighter sphere) m/s (heavier sphere) (b) If the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? (Note: Assume a reference level of potential V = 0 at r = ∞.) less than the same greater Explain your answer.

Answer 1

(a)

The bodies interact through the gravitational force and electrostatic force. But Since

Gravitational force of interaction can be neglected compared to electrostatic force of interaction.

Since the spheres are insulating, charges do not move during the motion of spheres.

Since there are no external forces the momentum of the spheres can be conserved.

Initial momentum is zero.

Energy of system can also be conserved.

Initial energy (initial kinetic energy of spheres is zero)

Final energy

Initial distance between the centres of spheres

Final distance between the centres of spheres

Hence the spheres will be moving with speeds   and in opposite directions towards each other.

(b)

If the spheres are conducting, the charge distribution on them cannot be taken to be uniform always.

When the spheres are faraway (initially) the charge distribution will be uniform. But when the spheres are close to each other the charges on them will be mostly on the parts of surfaces nearer to each other. Hence the effective distance between them will be less than sum of radii. .

Hence the spheres will be travelling with speeds greater than those calculated in part (a).