A hollow smooth tube of mass 2 m is lying at rest on a smooth horizontal surface between two smooth parallel vertical walls as shown in the figure. A small smooth ball of mass m moving with velocity u

Question

A hollow smooth tube of mass 2 m is lying at rest on a smooth horizontal surface between two smooth parallel vertical walls as shown in the figure. A small smooth ball of mass m moving with velocity u enters into the tube. [All observations are to be made w.r.t ground] Maximum KE of the tube is

TestHub · Accepted Answer

Horizontal momentum of system is conserved parallel to the walls. KE of tube is maximum when the ball and tube get common velocity.

$m u = (3 m) V_{c} \Rightarrow V_{c} = \frac{u}{3} K E_{m a x} of the tube = \frac{1}{2} (2 m) V_{c}^{2} = \frac{m u ^{2}}{9}$

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JEE Advanced (2028)