Q146 / 180 · AIIMS 2018 (26 May) · Physics

With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$, so that it may reach the top of the tube? Radius of the tube is $R$. (Assume radius of cross-section of tube is negligible in comparison to $R$.) Figure

  • A
    $\sqrt{2 g(h+2 R)}$
  • B
    $\frac{5}{2} R$
  • C
    $\sqrt{g(5 R-2 h)}$
  • Correct answer
    D
    $\sqrt{2 g(2 R-h)}$

Solution

For minimum $v$, velocity of ball at the topmost point will be zero. Byconservationof energy, $\frac{1}{2} m v^2=m g(2 R-h)$ $v=\sqrt{2 g(2 R-h)}$

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

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