A cubic block of side a is connected with two similar vertical springs as shown. Initially, bottom surface of the block of density `sigma` touches the surface of the fluid of density `2sigma` while floating. A weight is placed on the block so that it is immersed half in the fluid, find the weight.

Options

A. `a(K/2=a^(2)sigmag)`
B. `a(K+a^(2)sigmag)`
C. `a(K+a^2/2sigmag)`
D. `a/2(K+a^(2)sigmag)`

Answer

B

Explanation

Initially `W-2Kx=0` ………i
Finally `W'-2K(x+a/2)-a.a.a/22sigma.g=0`..ii
`W'=W+W_(0)`
`W+W_(0)-2Kx-ka-a_(3)rhog=0` [from eqn ii]
from eqn i
`W_(0)=Ka+a^(3)sigmag=a(K+a^(2)sigmag)`