JEE Mains · Physics · STD 11 - 13. oscillations
A cylindrical block of mass M and area of cross section A is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________ .
- A \(2 \pi \sqrt{\frac{ M }{\rho Ag }}\)
- B \(\pi \sqrt{\frac{2 M }{\rho Ag }}\)
- C \(\pi \sqrt{\frac{\rho A }{ Mg }}\)
- D \(2 \pi \sqrt{\frac{\rho A}{ Mg }}\)
Answer & Solution
Correct Answer
(A) \(2 \pi \sqrt{\frac{ M }{\rho Ag }}\)
Step-by-step Solution
Detailed explanation
At equilibrium \(\rho Ahg = Mg\) After displacing by x , \(M a=-\rho A(h+x) g+M g\) \(M a=-\rho A h g-\rho A x g+M g\) \(Ma =-\rho Axg\) \(a=\left(\frac{-\rho A g}{M}\right) x\) on comparing with, \(a=-\omega^2 x\) \(\omega=\sqrt{\frac{\rho Ag }{ M }}\)…
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