Question

A wooden cube floating in water supports a mass 0.2 kg on top of it. When the mass is removed, the cube rises by 2 cm. What is the edge length of the cube? Density of water = ${10}^{3}kg/m^3$

• A. 5 cm
• B. 15 cm
• C. 10 cm
• D. 8 cm

Answer 1

The correct option is C 10 cm

m = 0.2 kg = 200 g
Let the edge length of the cube be ‘a’
mg + weight of cube = upward thrust
$200g+VDg=V\times d\times g$
$200+a^{3}D=a^3\times 1$
$a^{3}D=a^3–200$---(1)

Weight = upward thrust of the cube
Vdg = V’dg
$a^{3}D=a^2(a-2)\times 1$
Taking value from--------(1)
$a^3-200=a^3-2a^2$
$200=2a^2$
$\sqrt{a^2}=\sqrt{100}$
$a=10cm$