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 :
Answer & explanation
Correct answer: option 1
Consider a small mass element dm at distance x from axis
$ dm = \frac{M}{L}dx$
force acting on small element of length dx is $dF = dm \omega^2 x$
Required force F = ∫dF = ∫ ω2 x(dm) = ∫L0 \(\frac{M}{L}\omega^2 x dx = \frac{M\omega^2L}{2}\)