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Question:

Two particle, of masses M and 2M, moving as shown, with speeds of 10m/s and 5m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds v1 and v2, respectively. The values of v1 and v2 are nearly:

6.5m/sand3.2m/s

6.5m/sand6.3m/s

3.2m/sand6.3m/s

3.2m/sand12.6m/s

Solution:

Correct option is C.
6.5m/sand6.3m/s
M × 10cos30° + 2M × 5cos45° = 2Mv1cos30° + Mv2cos45°
5√3 + 5√2 = 2v1√3/2 + v2√2/2
10Msin30° - 2M × 5sin45° = Mv2sin45° - 2Mv1sin30°
5M - 5√2M = Mv2√2/2 - Mv1
5 - 5√2 = v2√2/2 - v1
Solving v1 ≈ 6.5m/s
v2 ≈ 6.3m/s