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 froces as (1) Spring force \[{{K}_{x,}}\] where X = elongation of the spring. (2) Gravitational force \[{{F}_{b}}\] (or upward thrust) imparted. (3) Byoliant 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 \[{{K}_{x}}+{{F}_{b}}=mg\] \[\Rightarrow \] \[X=\frac{mg-{{F}_{b}}}{R}=\frac{mg-Vdg}{K}\] Where, \[V=(m/D)\] \[X=\frac{mg}{K}\,\,\left( 1-\frac{d}{D} \right)\]You need to login to perform this action.
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