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BITSAT2018PhysicsCenter of Mass, Momentum and CollisionActual

A trolley having mass of 200 kg moves with uniform speed of 36 kmh - 1 on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other ( 10 m away) with a speed of 4 m s - 1 relative to the trolley in a direction opposite to its inotion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?

Options

  1. A10 . 36   m   s - 1
  2. B11 . 36   m   s - 1
  3. C12 . 36   m   s - 1
  4. D14 . 40   m   s - 1

Correct answer

A. 10 . 36   m   s - 1

Step-by-step solution

since, no external force is acting on the system, we can apply conservation of linear momentum. Speed of 200   kg trolley = 36 × 1000 60 × 60 = 10   m   s - 1 If u be the initial velocity of trolley, v b be the absolute velocity of the boy after the beginning of journey of the boy, their relative velocity is 4 . So, v ' - v b = 4 ⇒ v b = v ' - 4 Now, applying law of conservation of momentum, Momentum before the boy begins tu run = Momentum after the beginning of boy's runn

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