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Q.

_{A cylindrical vessel of radius 2R contains a cylinder of length} $l$ _{, radius ‘R’ is floating in water half submerged. Now the cylinder is pushed a little in vertical direction and released. It performs oscillations on water surface. Frequency of oscillations ‘f ’ is}

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a

$f = \sqrt{\frac{3 g}{8 π^{2} l}}$

b

$f = \sqrt{\frac{g}{2 π^{2} l}}$

c

$f = \sqrt{\frac{2 g}{3 π^{2} l}}$

d

$f = \sqrt{\frac{3 g}{16 π^{2} l}}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

$m = \frac{2}{3} π R^{3} ρ_{w}$ -----------(1)

Let ‘x’ be displacement of sphere $π R^{2} (1 + \frac{π R^{2}}{3 π R^{2}}) x ρ_{w} g = m \ddot{x} =$ Restoring

force ----------(2)

$f = \sqrt{\frac{2 g}{3 π^{2} R}}$

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A cylindrical vessel of radius 2R contains a cylinder of length l , radius ‘R’ is floating in water half submerged. Now the cylinder is pushed a little in vertical direction and released. It performs oscillations on water surface. Frequency of oscillations ‘f ’ is