A tube of length 1 m is filled completely with an ideal liquid of mass 2 M, and closed at both ends. The tube is rotated uniformply in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity o

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Solution

Q.
A tube of length 1 m is filled completely with an ideal liquid of mass 2 M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\frac{F}{α M}}$ in SI unit. The value of $α$ is __________. [2025]

Ans.
(1)

$F = 2 M ω^{2} r_{cm} where, r_{cm} = \frac{l}{2}$

$F = 2 M ω^{2} \frac{l}{2} = M ω^{2} l$

$\Rightarrow α = 1$ .

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