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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.
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B
2.7 g
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C
16.8 g
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D
8.1 g
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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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