SHMHard
Question
A uniform cylinder of length L and mass M having cross-section area A is suspended, with its length vertical from a fix point by a mass less spring, such that it is half-submerged in a liquid of density ρ at eqilibrium positions. When the cylinder is given small downwards push and released it starts oscillating vertically with a small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is
Options
A.
B.
C.
D.
Solution
When cylinder is displaced by an amount x from its mean position, spring force and upthrust both will increase. Hence,
Net restoring force = extra spring force + extra upthrust
or F = - (kx + Axρg)
or a = -
Now f =
= 
∴ Correct answer is (b).
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