A bubble is at the bottom of the lake of depth h. As the bubble comes to sea level, its radius increases three times. If atmospheric pressure is equal to `I` metre of water column, then h is equal to

Options

A. 26 l
B. l
C. 25 l
D. 30 l

Answer

A

Explanation

Assuming temperature constant
As from the Boyle's law Pv=constant
So, from the two cases at h depth and at the surface `p_(1)V_(1)=p_(2)V_(2)....(i)`
Where, `p(1)`=pressure at h depth, `V_(1)`=volume at h depth
`p_(2)` =pressure at surface, `V_(2)` =volume at surface
`p_(1)=(h+l)pg,V_(1)=(4)/(3)pir^(3)`
`p_(2)=lpg,V_(2)=(4)/(3)pi(3r)^(3)`
Putting these values in Eq. (i), we get
`(h+l)pg((4)/(3))pir^(3)=lpgxx((4)/(3))pi(3r)^(3)`
`So, (h+l)=27l`
`Rightarrow h=26l`