A cubical block of wood of edge a and density `rho` floats in water of density `2rho`. The lower surface of the cube just touches the free end of a mass less spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

Options

A. ` a (a^2 rho g + K ) `
B. ` a (a rho g + 2 K ) `
C. ` a ( ( arho g )/(2) + 2K ) `
D. ` a (a^2 rho g + (K ) /(2) ) `

Answer

D

Explanation

` (##VMC_PHY_XI_WOR_BOK_02_C08_E02_017_S01.png" width="80%">
` rArr `Density of block = 1/2 (density of water)
W = Extra upthust + Spring force
` rArr a xx a xx (a)/(2) 2 rho xx g + K ((a )/(2)) rArr a (a ^ 2 rho g + (K)/(2)) `