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 restoring force acting on it is

Options

A. `mg cos theta`
B. `(mg)/(cos theta)`
C. `mg[(1)/(cos theta)-1]`
D. `mg[(1)/(cos theta)+1]`

Answer

C

Explanation

Let `l` be the length of the cylinder, when verticlal in water. Let `A` be the cross-sectional area of the cylinder. Equanting weight of the cylinder with the upthrust, we get
`Mg = A l rho g or m=Alrho`
When the cylinder is titled through an angle `theta`, length of cylinder in water =`l=(cos theta)`
weight of water displaced = `(l)/(cos theta) A rho g`
Restoring force = `(lA rho g)/(cos theta) -lArhog`
`=lArhog [(1)/(costheta)-1]=mg[(1)/(costheta)-1]`.