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 mass less spring of constant k. The cylinder is half submerged in s liquid of density ρ. A small push and release make it vibrate with small amplitude. The frequency of oscillation is
Options
A.
B.
C.
D.
Solution
Initially 
Finally
Vg
kx + FB = mg
kx = mg - ρVg
kx = mg -
.............(i)
Let cylinder be displacement through then restoring force,
fnet = - [k(x + y) + FB - mg]
fnet = -
fnet = - [ky + ρAgy] ⇒ ma = -[ky + ρAgy]
⇒ ω =
FinallyVgkx + FB = mg
kx = mg - ρVg
kx = mg -
.............(i)Let cylinder be displacement through then restoring force,
fnet = - [k(x + y) + FB - mg]
fnet = -
fnet = - [ky + ρAgy] ⇒ ma = -[ky + ρAgy]
⇒ ω =
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