Correct Answer - C
`p_(1)=p_(2)`
`p_(0)+pg(L_(0)-H)=p` (i)
Now, applying `p_(1)V_(1)=p_(2)V_(2)` for the air inside the cylinder, we have
`p_(0)(L_(0))=p(L_(0)-H)`
`p=(p_(0)L_(0))/(L_(0)-H)`
Substituting in Eq. (i), we have
`p_(0)+pg(L_(0)-H)=(p_(0)L_(0))/(L_(0)-H)`
`implies pg(L_(0)-H)^(2)+P_(0)(L_(0)-H)-L_(0)p_(0)=0`
Therefore, option `(c)` is correct.