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A cubical block of wood of edge a and de...

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

A

`a(a^(2)rhog+k)`

B

`a(arhog+2k)`

C

`a((arhog)/(2)+2k)`

D

`a(a^(2)rhog+(k)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, density of block `=1//2` (density of water),
`50%" of its volume is immersed in water."`
In the second case, half of the volume of the block is further immersed in water
`W="Extra up thrust "+"spring force"`
`=axxaxx(a)/(2)xx2rho xxg+k(a)/(2)=a(a^(2)rhog +(k)/(2))`
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