A) \[\frac{mg}{k}\left( 1-\frac{d}{D} \right)\]
B) \[\frac{mg}{k}\left( 1-\frac{D}{d} \right)\]
C) \[\frac{mg}{k}\left( 1+\frac{d}{D} \right)\]
D) None of these
Correct Answer: A
Solution :
The cube is in equilibrium under three forces as, Spring force \[kx,\] where \[x=\] elongation of the spring, Gravitational force \[w,\] weight of the cube = \[=mg\] 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, \[kx+{{F}_{b}}=mg\] \[\Rightarrow \] \[x=\frac{mg-{{F}_{b}}}{k}\] \[=\frac{mg-Vdg}{k}\] where, \[V=\left( \frac{m}{D} \right)\] \[\Rightarrow \] \[x=\frac{mg}{k}\left( 1-\frac{d}{D} \right)\]You need to login to perform this action.
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