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Question

The system shown in the adjacent figure is in equilibrium. The mass of the container with liquid is M, density of liquid in the container is ρ and volume of the block is V. If the container is now displaced downwards through a distance x0 and released such that the block remains well inside the liquid, then during subsequent motion.

A
time period of SHM of the container will be 2πMk
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B
time period of SHM of the container will be 2π(M+pv)k
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C
amplitude of SHM of the container will be greater than x0
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D
container will not perform SHM
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Solution

The correct option is B time period of SHM of the container will be 2π(M+pv)k
Mgk(x+Δx)+ρ(V)(ga)=Ma
Where Mg+pVg=kΔx
(M+ρV)a=Kx
Or a=kx(M+ρV) or ω=kM+ρV
T=2π(M+ρV)k

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