Question

Some iron beads are embedded in wax ball which is
just floating in water. The volume of ball is 18 cm
and relative density of wax is 0.9. Then mass of the
iron trapped in the ball is
(a) 188 (b) 2.7 g (c) 16.8 g (d) 8.18​

Answer 1

mass of iron trapped in the spherical ball is 1.8 g

volume of ball, V_(ball) = 18cm³

relative density of wax = 0.9

as we know density of water , ρ_(water) = 1g/cm³

so, density of wax , ρ_(wax) = 0.9g/cm³

according to Archimedes theorem,

condition of floating,

weight of wax + weight of iron = weight of water displaced by sphere

⇒V_(sphere)ρ_(wax)g + m_(iron)g = V_(sphere)ρ_(water)g

[ as V_(wax) ≈ V_(sphere)]

⇒18 cm³ × 0.9g/cm³ + m_(iron) = 18cm³ × 1g/cm³

⇒m_(iron) = 18 - 18 × 0.9 = 1.8 g

hence, mass of iron trapped in the spherical ball is 1.8 g

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