A vessel has water to height of 40 cm. it has three horizontal capillary tubes of same diameter each of length 15 cm coming out at height 10 cm, 15 cm, 20 cm .The length of a single tube of same diameter as that of the three tubes which can replace them when placed horizontally at the bottom of the vessel is:

Options

A. 45 cm
B. 5 cm
C. 8 cm
D. 16 cm

Answer

C

Explanation

`h` is total height of water `h_(1),h_(2),h_(3)` are the heights at which tubes are fitted
`Q_(1)=(pi(h-h_(1))dgr^(4))/(8etal),Q_(2)=(pi(h-h_(2))dgr^(4))/(8etal)`
`Q_(3)=(pi(h-h_(3))dgr^(4))/(8etal) and Q=Q_(1)+Q_(2)+Q_(3)`
With `Q=(pihdgr^(4))/(8etal),(h)/(l)=(h_(1))/(l_(1))+(h_(2))/(l_(2))+(h_(3))/(l_(3))`