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

Answer 1

Answer: (A)

1.8 g.

Volume of ball, $V_{ball}=18c{m}^3$

Relative density of the wall $=0.9$

As we know,

Density of water, ${\rho }_{water}=1g/c{m}^3$

So,

Density of wax, ${\rho }_{wax}=\mathrm{0.9.}g/c{m}^3$

According to Archimedes theorem. condition of floating,

Weight of wax $+$ Weight of iron $=$ Weight of water displaced by sphere

$⟹V_{sphere}\rho +waxg+m_{iron}g=V_{sphere}{\rho }_{water}g$

As $V_{max}\approx V_{sphere}$

$⟹18\times 0.9+m_{iron}=18\times 1$

$⟹m_{iron}=18-18\times 0.9=1.8g$

Hence, mass of iron trapped in the spherical ball is $1.8g$.