A) \[T=2\pi \sqrt{\frac{m}{3\rho gA}}\]
B) \[T=2\pi \sqrt{\frac{m}{2\rho gA}}\]
C) \[T=2\pi \sqrt{\frac{m}{\rho gA}}\]
D) None of these
Correct Answer: A
Solution :
[a] Suppose the liquid in left side limb is displaced slightly by y, the liquid in right limb will increase by \[y/2\]. The restoring force \[F=-PA=-\rho g\left( \frac{3y}{2} \right)\times 2A=3\rho gA(-y)\]. \[a=\frac{F}{m}=3\rho gA(-y)/m\] On comparing with, \[a=-\,{{\omega }^{2}}y\], we get \[\omega =\sqrt{\frac{3\rho gA}{m}}\] and \[T=2\pi \sqrt{\frac{m}{3\rho gA}}\]You need to login to perform this action.
You will be redirected in
3 sec