Question

A solid cube of side $a=5cm$ has a mass of $M=1000g$. It is recasted into a hollow cube of side $b$ with air inside. What should be the minimum value of $b$, so that this hollow cube floats in this water?
Consider air mass in cylinder to be negligible.

• A. $b=5cm$
• B. $b=8cm$
• C. $b=10cm$
• D. $b=20cm$

Answer 1

The correct option is C $b=10cm$

In order to float, the density of the object must be equal to or less than water.
In order to float, the density of hollow cube has to be less than or equal to the density of water.
Density of hollow cube:
$\rho =\frac{M}{V}\le {\rho }_w$
$\frac{1000}{b^3}\le 1$
$b\ge 10cm$