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 and is left. The restoring force acting on it is

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Solution

The correct option is C

l = length of cylinder

A = Area of crossection of cylinder

mg = (A) (l) ( $ρ$ ) (g)

m = Al $ρ$

When cylinder is tilted through an angle

length of cylinder in water = $\frac{1}{c o s θ}$

wt of water displaced = $\frac{l}{c o s θ} A ρ g$

restoring force = $\frac{l A ρ g}{c o s θ} - l A ρ g$

= $l A ρ g (\frac{1}{c o s θ} - 1) = m g (\frac{1}{c o s θ} - 1)$

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