SHMHard

Question

A uniform cylinder of mass m and length l having area of cross-section a is suspended lengthwise with the help of a massless spring of force constant k. The cylinder is half submerged in a liquid of density ρ as shown in figure. A small push and release makes it vibrate with small amplitude. The frequency of oscillation is :

Options

A.
B.
C.
D.

Solution


If cylinder is displaced x vertically down as shown then Net force on cylinder
F = kx + x.a.ρg
m = (k + aρg) x           ⇒ = ω2x = (2πn)2  x
So frequency n =

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