Question

A cubical wood of sides 20cm has a density of 0.25 g/cm³ . If it is kept in the water, find the ratio of length of the wood above the water to the length of the wood below the water. ( g= 10m/s² )

• A. 2 : 1
• B. 1 : 1
• C. 3 : 1
• D. 1 : 3

Answer 1

The correct option is C

3 : 1

Volume of the block = 20$\times$ 20 $\times$ 20=8000 $c{m}^3$
Mass of the block = 0.25 $\times$ 8000 = 2000g=2kg
Downward force = 20N
And it should be equal to weight of water displaced.
$\Rightarrow$ 20 = $M_{waterdisplaced}\ast$ g = Volume displaced $\ast$ Density $\ast$ g
$\Rightarrow$ 20 = 20 $\ast$ 20 $\ast$ H $\ast$ 1 $\ast \frac{10}{1000}$ (divided by 1000 as mass will come in 'g')
$\Rightarrow$ 20 = 4 $\ast$ H
$\Rightarrow$ H = 5cm
Ratio = $\frac{(20-5)}{5}=\frac{3}{1}$