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JEE Main202528 Jan 2025Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3 a^ will be (Take ' g ' as acceleration due to gravity)

Options

  1. A2 Ma 3 a + g
  2. B3 Ma 2 a - g
  3. C3 Ma 2 a + g
  4. D2 Ma 3 a - g

Correct answer

A. 2 Ma 3 a + g

Step-by-step solution

aligned & F-m g=m a & F=m a+m g & F-(m-x) g=(m-x) 3 a aligned Put F aligned & Ma + mg - mg + xg =3 ma -3 xa & x = 2 ma ~g +3 a aligned

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