Fluid Mechanics Viscosity Question 276
Question: A uniform wooden stick of length L, cross- section area A and density d is immersed in a liquid of density 4rf. A small body of mass m and negligible volume is attached at the lower end of the rod so that the stick floats vertically in stable equilibrium then
Options:
A) $ m > dAL $
B) $ m<dAL $
C) $ m<dAL/2 $
D) $ m<dAL/4 $
Show Answer
Answer:
Correct Answer: A
Solution:
For equilibrium $ 4dA\ell g=(dAL+m)g $ and$ \frac{\ell }{2}>Y_{cm} $ (for rotational equilibrium) $ Y_{cm}=\frac{m\times 0+dAL(L/2)}{m+dAL}=\frac{dAL^{2}}{2(m+dAL)} $ $ \ell >\frac{AL^{2}d}{(ALd+m)}\Rightarrow \frac{m+dAL}{4dA}>\frac{AL^{2}d}{(ALd+m)} $ $ m>ALd $
BETA
