question_answer

A bent tube of uniform cross-section area A has a non-viscous liquid of density p. The mass of liquid in the tube is m. The time period of oscillation of the liquid is  

A) \[2\pi \sqrt{\frac{m}{\rho gA}}\]

B) \[2\pi \sqrt{\frac{m}{2\rho gA}}\]

C) \[2\pi \sqrt{\frac{2m}{\rho gA}}\]

D) None of these

Correct Answer: A

Solution :

[a] The restoring force \[F=-(PA)\] \[=-[\rho g(2y\sin {{30}^{o}})]A\] \[=\rho gA(-y)\] \[\therefore \,\,\,\,a=\frac{F}{m}=\frac{\rho gA}{m}\]  Thus   \[T=2\pi \sqrt{\frac{m}{\rho gA}}\]