SATHEE: Properties Of Solids And Liquids Question 258

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 $θ$ and is left. The respecting force acting on it is

Options:

A) $m g \cos θ$

B) $\frac{m g}{\cos θ}$

C) $m g [\frac{1}{\cos θ} - 1]$

D) $m g [\frac{1}{\cos θ} + 1]$

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 $M g = A l ρ g o r m = A l ρ$

When the cylinder is tilted through an angle $θ$ , length of Cylinder in water $= \frac{1}{\cos θ}$

Weight of water displaced $= \frac{l}{\cos θ} A ρ g$

Restoring force $= \frac{l A ρ g}{\cos θ} - l A ρ g$

$= l A ρ g [\frac{1}{\cos θ} - 1] = m g [\frac{1}{\cos θ} - 1]$

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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 θ and is left. The respecting force acting on it is

Options:

Answer:

Solution:

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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 $θ$ and is left. The respecting force acting on it is