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JEE Main Physics question

PhysicsWork, Energy and PowerJEE Main

A bob of mass m, suspended by a string of length l₁, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l₂, which is initially at rest. Both the strings are massless and inextensible. If the second bob, after collision, acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l₁/l₂ is

Answer: 5

Solution

The minimum speed to complete a vertical circle of radius R is √(gR). So the first bob's speed at the highest point is v₁ = √(gl₁). Since the masses are equal and the collision is elastic, the velocities are exchanged — the second bob acquires speed v₁ = √(gl₁) after collision. For the second bob

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Question ID VK-154209