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A cubical body (side 0.1m and mass 0.00...

A cubical body (side `0.1m` and mass `0.002kg)` floats in water. It is pressed and then released so that it executes SHM. Find the time period. `(g=10m//s^(2))`

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Let cubical body be floating in water of density `sigma` with length l inside the water. Then
weigth of body `=` upward thrust due to water
so `mg=Alsigmag or m=Alsigma` …(i)
If the cubical body is depressed through distance y, then effective restoring force on the body is
`F=-[A(l+y)sigmag-Alsigmag]=-(Asigmag)y` …(ii)
As , `Fproy` and this F is directed towards equilibrium position of body, so the body when released will execute linear SHM.
Here, spring factor `=Asigmag,` inertia factore `=m`
Time period, `T=2pisqrt(("inertia factor")/("spring factor"))=2xx(22)/(7)sqrt((m)/(Asigmag))=2xx(22)/(7)sqrt(((0.002))/((0.1)^(2)xx10^(3)xx10))=0.028s`
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