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A uniform cylinder of length $\mathrm{L}$ and mass $M$ having cross-sectional area $\mathrm{A}$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period $\mathrm{T}$ of the oscillations of the cylinder will be :
PhysicsOscillationsJEE MainJEE Main 2013 (25 Apr Online)
Options:
  • A
    Smaller than $2 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}$
  • B
    $2 \pi \sqrt{\frac{M}{k}}$
  • C
    Larger than $2 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}$
  • D
    $2 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}$
Solution:
2454 Upvotes Verified Answer
The correct answer is:
Smaller than $2 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}$
No solution is given.

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