A cylinder 2m in diameter and 10 m log floats in FW, with its axis horizontal, at draft of 0.6m. Find its mass.
Diameter of cylinder= D = 2m,
Radius = ( D / 2 )
length = 10m, depth = 0.6m
Mass = (u/w volume) x (density of displaced water)
Weight = ( πr2h x density )
= (3.1416 x 1 x 1 x 0.6) x (1)
A barge of triangular cross section is 20m long, 12m wide and 6m deep. It floats in SW at a draft of 4m. Find its displacement.
Volume of triangular cross section = (L x B X H )
= (20 x 12 x6)
Depth = 4m
Here Displacement means = displacement by triangular cross section.
In triangle ABC, CG is perpendicular to AB
So triangle GBC and EFC are similar,
So by law of similar angle triangle
GB / EF = GC / EC
6 / EF = 6/ 4
EF = (6x 4)/6
Now, DF = (2EF)
Displacement = ( u/w volume ) x (1.025)
= (20 x 8 x 4) x (1.025)
= 656 t .
A cylindrical drum of 1.2m diameter and 2m height floats with it axis vertical in water of RD 1.016 at a draft of 1.4m. Find the maximum mass of lead shots that can be put in it with sinking it.
Radius = (d/2)
H = 2m, D =1.4m , RD = 1.016
Mass of the cylinder = (r2 h) x(density)
= (3.1416 x 0.6 x 0.6 x 2) x (1.016)
Mass of the cylinder at 1.4m = 1.4 x r2 h) x (density)
= 1.4 x (3.1416 x 0.6 x0 .6) x (1.016)
= 1.608 t
Hence ,the maximum mass of lead shots that can be put in it with sinking is (2.298 t – 1.608 t) = 0.69 t