Question

A $700g$ solid cube having an edge of length $10cm$ floats in water. The volume of cube outside water is:

• A. $2.4c{m}^3$
• B. $4.8c{m}^3$
• C. $300c{m}^3$
• D. $500c{m}^3$

Answer 1

Answer: (C)

When a solid body is immersed in a liquid, then there is some apparent loss in its weight.
Two forces act on the cube:
(i) weight (mg) of body (downwards)
(ii) upthrust (U) of liquid (upwards).
For floatation $U=mg$ Let $V$ be volume of cube inside liquid,
then $V\times d\times g=mgV\times 1000\times 10$
$=0.7\times 10$
$\Rightarrow V=\frac{7}{10.000}{m}^3=700c{m}^3$
Total volume of cube $=(10cm{)}^3=100c{m}^3$
Volume outside water $=1000-700=300c{m}^3$