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A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2:2:1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is

Asked in NEET 2022 · Discrete systems and motion of the centre of mass

• (1) v
• (2) √2 v
• (3) 2√2 v
• (4) 3√2 v

Step-by-step solution

Why the other options are wrong

• (1) comes from gives the light fragment the same speed as the other two; carrying half their mass it must move faster than either of them, not the same
• (2) comes from treating all three fragments as equally massive, so the resultant √2 μ v is divided by μ rather than by the smaller mass
• (4) comes from no single slip reproduces 3√2 v; it would need the light fragment to carry 3√2 kv of momentum, half as much again as the 2√2 kv the other two actually supply

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