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Question

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g/cm3. If the mass of the other is 48 g, its density in g/cm3 is

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Solution

Given,
Mass of the body, m=36 g

Density of the body, p=9 g/cm3

Density of water, σ=1 g/cm3

As we know, if two bodies are in equilibrium, it means both bodies have equal apparent weights. Therefore,

Apparent weight
=V(pσ)g=mp(pσ)g

m1p1(p1σ)=m2p2(p2σ)

369(91)=48p2(p21)

p2=3

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