Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.400 kg and 0.7

Question

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.400 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 = .)

greater

the same    

less than

Explain your answer.

Explanation / Answer

From momentum conservation, m1v1= m2v2 as total momentum is zero for the system. But v1 and v2 will be in opposite directions.

Now from energy conservation change in potential energy is same as change in kinetic energy will opposite signs.

KQ1Q2(1/r2 - 1/r1) = 1/2m2v2(m2/m1+1).

Using v1 = m2v2/m1

0.620J = 0.9625v2 square

Hence v2 = 0.8025 m/s.

Hence v1 = 1.404 m/s

Heavier charge will move with lesser velocity and vice versa.

There will be no effect of conducting or insulating as we are treating outside which will be same. As placed at centre

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