A tube of length \(\mathcal{L}\) is filled completely with …

Physics Motion in a Plane Mix Single Correct MCQ

Published on: September 12, 2026

A tube of length \(\mathcal{L}\) is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\alpha\) . The force exerted by the liquid at the other end is

\(\frac{ML \omega^{2}}{2}\)

\(ML \ \omega^{2}\)

\(\frac{ML \omega^{2}}{4}\)

\(\frac{ML^{2}\omega^{2}}{2}\)

Text Solution

Verified by Experts

The correct answer is:

\(dM = \left(\frac{M}{L}\right) dx\)

force on ‘ dM ’ mass is

\(dF = (dM) \omega^{2} x\)

By integration we can get the force exerted by whole liquid

⇒ ⇒ \(F = \int_0^L \frac{M}{L} \omega^2 x \, dx\) \(= \frac{1}{2} M \omega^{2} L\)

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