A 100 g sphere is moving at a speed of 20 m/s and collides with anothe

For any collision in an isolated system, momentum is conserved.
Conservation of Momentum: m1*u1 + m2*u2 = m1*v1 + m2*v2
(0.1 kg) * (20 m/s) + (0.05 kg) * (0 m/s) = (0.1 kg) * (0 m/s) + (0.05 kg) * v2
2 + 0 = 0 + 0.05 * v2
2 = 0.05 * v2
v2 = 2 / 0.05 = 2 / (5/100) = 2 * (100/5) = 2 * 20 = 40 m/s.

While the question states the collision is elastic, the conditions provided (m1=100g, m2=50g, u1=20m/s, u2=0, v1=0) are mathematically inconsistent with a perfectly elastic collision. For an elastic collision with u2=0, v1 = ((m1 – m2) / (m1 + m2)) * u1. Substituting the values, v1 = ((0.1 – 0.05) / (0.1 + 0.05)) * 20 = (0.05/0.15) * 20 = (1/3) * 20 = 20/3 m/s, which is not 0. This means that either the collision was not elastic, or the first sphere did not come to rest.
However, given the multiple-choice format and the need to derive one of the options, the value v2 = 40 m/s is obtained directly from the conservation of momentum equation using the provided initial and final states. It is common in flawed physics problems in exams that one must rely on the most directly applicable principle (momentum conservation) and the given numbers, even if they contradict another stated condition (elasticity). Therefore, assuming the initial conditions and the final velocity of the first sphere are as stated, and momentum is conserved, the speed of the second sphere is 40 m/s.