Question

a block of wood of length 50 cm and area of cross section 10 cm2 floats in water with 3/5 of its length above water calculate density of wood in g cm -3
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Answer 1

Density of wood in given wooden block is 0.4 gram per cubic centimetre.

Explanation:

Given :

Cross sectional area of wooden block (A) = 10 square cm.

Length of given wooden block (L) = 50 cm

Fraction of wooden block's length floating above water = 3/5

To find : density of wood (in grams per cubic centimetre units)

Step by Step Solution :

Step-1 : Since Volume of wooden block (V) = Cross Sectional Area (A) x Length (L), calculate volume (V) as follows : V = A x L = 10 x 50 = 500 cu. cm.

Step-2 : Since 3/5th portion of wooden block's length is floating above water, its portion immersed in water = 1 - (3/5) = 2/5

Step-3 : Volume of wooden block immersed in water = (2/5) x 500 = 200 cubic cm.

Step-4 : Volume of wooden block immersed in water = Volume of water displaced by it = 200 cubic cm. (by Buoyancy Law)

Step-5 : Mass of water displaced by wooden block = 200 grams (as per conversion factor Mass of 1 cubic cm of water = 1 gram)

Step-6 : As per buoyancy law mass of water displaced by wooden block = mass of wooden block = 200 grams

Step-7 : Density of given wooden block = Mass / Volume = 200 / 500 = 0.4 grams per cubic cm.

Answer 2

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