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A hollow cylinder of mass `m` made heavy at its bottom is floating vertically in water. It is tilteed from its vertical position through an angle `theta` and is left. The respecting force acting on it isA. `mg cos theta`B. `(mg)/(cos theta)`C. `mg[(1)/(cos theta)-1]`D. `mg[(1)/(cos theta)+1]` |
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Answer» Correct Answer - C 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]`. |
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