Question

# Some iron beads are embedded in wax ball which is just floating in water. The volume of ball is 18 cm$$^3$$ and relative density of wax is 0.9. Then mass of the iron trapped in the ball is then

A
1.8 g.
B
2.7 g
C
16.8 g
D
8.1 g

Solution

## The correct option is B 1.8 g.Volume of ball, $$V_{ball}=18\,cm^3$$Relative density of the wall $$=0.9$$As we know,Density of water, $$\rho_{water}=1\,g/cm^3$$So,Density of wax, $$\rho_{wax}=0.9.g/cm^3$$ According to Archimedes theorem. condition of floating,Weight of wax $$+$$ Weight of iron $$=$$ Weight of water displaced by sphere$$\implies V_{sphere} \rho+{wax} \,g+m_{iron} \,g=V_{sphere}\rho_{water}\,g$$As $$V_{max} \approx V_{sphere}$$$$\implies 18\times 0.9 +m_{iron}=18\times 1$$$$\implies m_{iron}=18-18\times 0.9=1.8\,g$$Hence, mass of iron trapped in the spherical ball is $$1.8\,g$$.Physics

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