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.

Question

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. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/04a6cb7ed27ffef87578645ac9c9984a-.png" /> (A) √2g(h+2R) (B) (5/2)R (C) √g(5R-2h) (D) √2g(2R-h)

Tardigrade Admin · Accepted Answer

Velocity of ball to just reach the top of the tube should be given by; 0=v2-2 g h0 Here h0 =(R-h) and in critical case velocity will be zero at topmost point. Thus v=√2 g(2 R-h)

Q. 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 $R .$

$2 g (h + 2 R)$

$\frac{5}{2} R$

$g (5 R - 2 h)$

$2 g (2 R - h)$

Velocity of ball to just reach the top of the tube should be given by;
$0 = v^{2} - 2 g h_{0}$
Here $h_{0} = (R - h)$
and in critical case velocity will be zero at topmost point.
Thus $v = 2 g (2 R - h)$

Q. 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.

2g(h+2R)​

25​R

g(5R−2h)​

2g(2R−h)​