A metallic cube of side 10 cm, density 6.98 gm/cc is floating in liquid mercury (density 13.6 gm/cc), with 5 cm height of cube exposed above the mercury level. Water (density 1 gm/cc) is filled over this to submerge the cube fully. The new height of cube exposed above mercury level is
- A. 4.6 cm
- B. 5.4 cm
- C. 5.0 cm
- D. 5.8 cm
Answer: B. 5.4 cm
Explanation: Let x be depth in mercury. Buoyancy balance: $6.8(10^3) = 13.6(100x) + 1(100(10-x))$. Solving gives $x \approx 4.6$ cm. Height exposed above mercury (in water) is $10 - 4.6 = 5.4$ cm.