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AP EAMCET201823 Apr 2018Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A rocket with an initial mass m₀ is going up with a constant acceleration a by exhausting gases with a velocity v relative to the rocket motion, then the mass of the rocket at any instant of time is (assume that no other forces act on it)

Options

  1. Am=m₀ e^ - a t v
  2. Bm=m_ e e^ - 2 a t v
  3. Cm=m₀ e^ - af 2 v
  4. Dm=m₀ e^ - a^2 t^2 v^2

Correct answer

A. m=m₀ e^ - a t v

Step-by-step solution

For a rocket, m d v d t =F_ ext +v d m d t Without any external force (F_ ext =0 ) , array ll & m d v d t =v d m d t d v v = d m m & v= m+C array When, v=0, m=m₀ C=- m₀ So, we have v v = m m₀ d t or m=m₀ e^ -a t / v

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