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NEET 2015 (AIPMT) · Collisions

Collisions question from NEET 2015 (AIPMT)

Q11NEET 2015 · AIPMTMedium

Collisions

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is

(Take g = 10 m s−2{}^{-2})

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Answer: (d)

  1. Energy at ground before impact: 12mv02+mgh\frac{1}{2}mv_0^2 + mgh
  2. Half is lost and the rest lifts it back to hh: 12(12mv02+mgh)=mgh\frac{1}{2}\left(\frac{1}{2}mv_0^2 + mgh\right) = mgh
  3. 12v02=gh⇒v0=2×10×20\frac{1}{2}v_0^2 = gh \Rightarrow v_0 = \sqrt{2 \times 10 \times 20}
  4. So the answer is (d) 20 m/s.
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