Q75 / 91 · KVPY 2018 (SB/SX) · Physics

Two balls of mass M and 2M are thrown horizontally with the same initial velocity v0 from top of a tall tower and experience a drag force of -kvk>0 where v is the instantaneous velocity.
Figure

Then,

  • Correct answer
    A
    the heavier ball will hit the ground further away than the lighter ball
  • B
    the heavier ball will hit the ground closer than the lighter ball
  • C
    both balls will hit the ground at the same point
  • D
    both balls will hit the ground at the same time

Solution

Only force resisting motion of particle in horizontal direction is drag force given by
F=-kv

But
F=m·ax

where, ax= acceleration in x-direction caused by drag force.
∴max=-kv⇒ax=-kvm

∴ Acceleration of particle is x-direction is inversely proportional to mass.
So, decreases in velocity in x-direction for lighter particle will be more.
Hence, heavier mass will hit the ground further away from the lighter ball.

Hence, the correct answer is option: 'A'.

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