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Density

a test tube f...

Question

A test tube floats in water with a small coin at its bottom. The mass of this test tube is equal to mass of seven coins and the external volume is $16 c m^{3}$ . It just sinks when third coin is added. Calculate the mass of each coin.

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Solution

Condition to just sink:
Let m = mass of each coin
d = density of water
V = volume of test tube
Weight of test tube + 3 coins = Buoyant force
Weight of test tube + 3 coins = Weight of water displaced by test tube
7mg + 3mg = Vdg
10mg = Vdg
10m = Vd
m = (Vd)/10 = (16x1)/10 =1.6 grams.

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