A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ 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 $T$ of the oscillations of the cylinder will be

Q: A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ 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 $T$ of the oscillations of the cylinder will be

a If $x$ is the displacement then, $M{\omega ^2}x = \left[ {\rho Ag + k} \right]x$ $ \Rightarrow \omega = {\left[ {\frac{{\rho Ag + k}}{m}} \right]^{1/2}}$ $ \Rightarrow T=2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$ It Should be less than $2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$

Question

ASmaller than $2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$
B$2\pi \sqrt {\frac{M}{k}} $
CLarger than $2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$
D$2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$

JEE MAIN 2013, Diffcult

Download our app
and get started for free

Similar Questions

Download our appand get started for free

Similar Questions

Download our app
and get started for free