Question

A tube of length 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 ω. The force exerted by the liquid at the other end is

• A. $\frac{ml\omega^{2}}{3}$
• B. mlω²
• C. $\frac{ml\omega^{2}}{2}$
• D. $\frac{ml\omega^{2}}{4}$

Answer 1

Answer: (C)

$\frac{ml\omega^{2}}{2}$

Answer 2

df = dmxω² = ρAdxw²

where A is area of cross – section

F = $\rho A\omega^{2}\int_{0}^{l}{xdx = \frac{\rho Ak^{2}\omega}{2} = \frac{ml\omega^{2}}{2}}${ $\rho A$l = m}