Rotational Kinematics & Dynamics question from NEET 2006 (AIPMT)

Answer: (b)

1. The end wall supplies centripetal force to all the liquid: $F = \int \omega^2 x\,dm$, with $dm = \dfrac{M}{L}dx$.
2. $F = \dfrac{M\omega^2}{L}\int_0^L x\,dx = \dfrac{M\omega^2}{L}\cdot\dfrac{L^2}{2}$
3. $F = \dfrac{ML\omega^2}{2}$, so the answer is (b).