Question

A cube (density $0.5gm/cc$ of side $10cm$ is floating in water kept in a cylindrical beaker of base area $1500c{m}^2$. When a mass $m$ is kept on wooden block the level of water rises in the beaker by $2mm$. The mass $m$ is

• A. $400gm$
• B. $300gm$
• C. $200gm$
• D. $100gm$

Answer 1

The correct option is B $300gm$

Draw a diagram of given problem.

Calculate volume of water displaced by block.
Given,
Base area of the block, $A=1500c{m}^2$

Height, $h=2mm=0.2cm$

Let the cube dips further by $ycm$ and water level rises by $2mm$.

Volume of water displaced,

$=[1500-(10\times 10\left)\right]\times \frac{2}{10}$

$=280c{m}^3$

Calculate mass m to rise water by $2mm$.
Volume of extra depth of wood,

$100\times y=100y$

Equating the volumes,

$100y=280$ $y=2.8cm$

Therefore, extra upthrust

$p_{water}\times (2.8+0.2)\times 100g=mg$

$m=300gm$