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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

Two bodies of the same mass are connected with an inelastic string of length l are placed together on a horizontal surface. One of them is projected vertically upwards from the surface with a velocity u = 6 gl . The maximum height up to which the centre of mass of the system of the two masses rises is

Options

  1. A3 l 4
  2. Bl 2
  3. C3 l 2
  4. Dl

Correct answer

D. l

Step-by-step solution

The velocity of B just before the string is taut v 1 = u 2 − 2 gl = 6 gl − 2 gl =2 gl After the string is taut, both will move up with same speed, v 2 = mv 1 m + m = v 1 2 = gl By this time centre of mass in at h = l 2 A further rise in the centre of mass = v 2 2 2 g = gl 2 g = l 2 Hence maximum height = l 2 + l 2 = l

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