Two capillary tubes of lengths in the ratio `2 : 1` and radii in the ratio `1 : 2` are connected in series. Assume the flow of the liquid through the tube is steady. Then, the ratio of pressure difference across the tubes is

Options

A. `1 : 8`
B. `1 : 16`
C. `32 : 1`
D. `1 : 1`

Answer

C

Explanation

We know that the pressure `p alpha (r^(4))/(l)`
`"Let" l_(1)=2l, l_(2)=l and r_(1)=r, r_(2)=2r`
`"Now", (p_(1))/(p_(2))=(r_(1)^(4))/(l_(1))xx(l_(2))/(r_(2)^(4))Rightarrow (p_(1))/(p_(2))=(r^(4))/(2l)xx(l)/((2r)^4)`
`(p_(1))/(p_(2))=(1)/(2xx(2)^(4)) Rightarrow (p_(1))/(p_(2))=(1)/(32)`