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A cube of mass m and density D is suspen...

A cube of mass `m` and density `D` is suspended from a point `P` by a spring of stiffness `k`. The system is kept inside a beaker filled with a liquid of density `d`. The elongation in the spring, assuming `D gt d`, is :

A

`(mg)/(k)(1-(d)/(D))`

B

`(mg)/(k)(1-(D)/(d))`

C

`(mg)/(k)(1+(d)/(D))`

D

None of these

Text Solution

Verified by Experts

The cube is in equilibrium under the following three forces,
`(A)` spring force `kx`, where `x=` elongation of the spring,
`(B)` gravitational force `w`, wieght of the cube `=mg`
`(C )` buoyant force `F_(b)` (or upward thrust) imparted by the liquid on the cube given as
`F_(b)=Vdg` where
`V=`volume of the immersed portion of the cube. For complete immersion, `V=` volume of the cube.
For equilibrium of the cube, `kx+F_(b)=mg`
`rArr x=(mg-F_(b))/(k)=(mg-Vdg)/(k)`, where `V=(m//D)`
`rArr x=(mg)/(k)(1-(d)/(D))`
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