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AP EAMCET202018 Sep 2020Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

At high altitude, a body explodes which is at rest into two equal fragments with one fragment receiving horizontal velocity of (10 ~ms ⁻¹ ). Time taken by the two radius vectors connecting point of explosion to fragments to make (90^ ) is

Options

  1. A(10 ~s )
  2. B(4 ~s )
  3. C(2 ~s )
  4. D(1 ~s )

Correct answer

D. (1 ~s )

Step-by-step solution

The given situation is shown in the following figure. According to question, angle between two radius vector is (90^ ). ( i.e., + =90^ =45^ ) ( ) Time taken by the two radius vectors connecting of explosion to fragments is (t ) second, then According to conservation of linear momentum, (m₁ v₁=m₂ v₂ m v₁=m v₂ v₁=v₂ ) Since, ( v ₁ ) and ( v ₂ ) are perpendicular to each other, hence ( aligned & v ₁ v ₂=0 & (-10 i -g j ) 10 i -g t j =0 & -100+g^2 t^2 =0 & x^2= 100 g^2 = 100 10^2 = ls aligned )

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