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))/(2)sigmag)`
D. `(a)/(2)(K+a^(2)sigmag)`

Answer

B

Explanation

Initially `W-2Kx=0` ..(1)
finally, `W^(')-2K(x+(a)/(2))-a.a.(a)/(2)2sigma.g=0` …(2)
`W^(')=W+W_(0)` `W+W_(0)-2Kx-Ka-a^(3)sigma.g=0`
[from eqn (2)] from eqn(1)
`W_(0)=Ka+a^(3)sigma=a(K+a^(2)sigmag)`