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UPSC Civil Service Exam Questions - Engineering

Q1:

A wooden plank (sp. gr. 0.5) 1 m x 1 m x 0.5 m floats in water with 1.5 kN load on it with 1 m x 1 m surface horizontal. The depth of plank lying below water surface shall be

A 0.178 m

B 0.250 m

C 0.403 m

D 0.500 m

ANS:C - 0.403 m

The wt of plank + wt of load = wt of fluid displaced.
(since wkt, wt = sp weight x Vol) (sp wt= density x g).

density x g x 1 x 1 x 0.5 + 1.5 x 1000 = 1000 x 9.81 x 1 x 1 x h.
( h= height of plank below the water level).

(1000 x 0.5 (sp gravity)) x 9.81 x 1 x 1 x 0.5 + 1.5 x 1000 = 1000 x 9.81 x 1 x 1 x h.
( since wkt, sp gravity = density of material / density of water).

Answer h=0.403.