Question

A cube of iron of edge $5cm$ floats on the surface of mercury, contained in a tank, Water is then poured on top, so that the cube just gets immersed. Find the depth of water layer. (Specific gravities of iron and mercury are $7.8$ and $13.6$, respecively.))

• A. 1 cm
• B. 1.8 cm
• C. 2 cm
• D. 2.2 cm

Answer 1

The correct option is D 2.2 cm

$p_{iron}=7.8,p_{mercury}=13.6$

By Archimedes principle,

$p_{iron}.(5\times 5\times 5).g=p_{mercury}.(5\times 5\times (5-x\left)\right).g+p_{water}(5\times 5\times x)$

$7.8\times 5^3=13.6\left(5^3\right)-13.6\times 25\times x+25x$

$x=\frac{5\times 58}{135}=2.148$

$x=2.15\sim x\approx 2.2㎝$