Properties Of Solids And Liquids Question 258
Question: A hollow cylinder of mass m made heavy at its bottom is floating vertically in water. It is tilted from its vertical position through an angle $ \theta $ and is left. The respecting force acting on it is
Options:
A) $ mg\cos \theta $
B) $ \frac{mg}{\cos \theta } $
C) $ mg\left[ \frac{1}{\cos \theta }-1 \right] $
D) $ mg\left[ \frac{1}{\cos \theta }+1 \right] $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let l be the length of the cylinder, when vertical, in water.
Let A be the cross-sectional area of the cylinder.
Equating weight of the cylinder with the up thrust, we get $ Mg=Al\rho gorm=Al\rho $
When the cylinder is tilted through an angle $ \theta $ , length of Cylinder in water $ =\frac{1}{\cos \theta } $
Weight of water displaced $ =\frac{l}{\cos \theta }A\rho g $
Restoring force $ =\frac{lA\rho g}{\cos \theta }-lA\rho g $
$ =lA\rho g\left[ \frac{1}{\cos \theta }-1 \right]=mg\left[ \frac{1}{\cos \theta }-1 \right] $
