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0.- A hollow sphere of inner radius r1 and outer radius r2 is submerged into a liquid of density 'l' as shown in figure. Find the density of sphere.
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Answer 1

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Since half of the body is floating, upward force = downward force (according to Archimedes principle)

Upward force = $\frac{2}{3}$ π r₂³ x l

Downward force = $\frac{4}{3}$ π (r₂ - r₁)³ x g x ρ

here, g= acceleration due to gravity

ρ = density of the sphere

since density of liquid is "l" gram/cm³

now by dividing the upward force and downward force, we will get

$\frac{r_1^3 x l}{2(r_2^3 - r_1^3)}$ = ρ

$\frac{r_1^3 x l}{2(r_2^3 - r_1^3)}$ is the density of the sphere

We got that 2 in the denominator, since 2/4 = 1/2 (please look at the above equations carefully)