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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

If two balls are tossed simultaneously into the air, the acceleration of their centre of mass while in flight

Options

  1. Adepends on the masses of the two balls
  2. Bis equal to g
  3. Cdepends on the direction of motion of the balls
  4. Ddepends on the speeds of the two balls

Correct answer

B. is equal to g

Step-by-step solution

Let the masses of the two balls be m₁ and m₂ . While in flight, the only force acting on each ball is gravity (ignoring air resistance). The acceleration of the first ball is a ₁ = g and the acceleration of the second ball is a ₂ = g . The acceleration of the centre of mass of the two balls is given by: a _ cm = m₁ a ₁ + m₂ a ₂ m₁ + m₂ Substituting a ₁ = g and a ₂ = g : a _ cm = m₁ g + m₂ g m₁ + m₂ = (m₁ + m₂) g m₁ + m₂ = g Thus, the acceleration of their centre of mass is equal to g downwards, independent of their

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