Name: Density of Substances
Uploaded: 2019-07-19
Duration: 6 min 34 s
Description: What is the density of a substance? Density is a very important thing to understand but is a bit tricky. Let’s fully grasp the idea of density from this video.

Question

A ferry boat has internal volume

1 m^{3}

and weight

50 kg

.

(a)

Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.

(b)

If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?

Accepted Answer

$(a)$ When the ferry floats on the water, let the volume of water displaced is $V$ .
According to the principle of floatation, the weight $(m g)$ of the ferry is balanced by the upward buoyant force $(a)$ .
So, $m g = V ρ_{w} g$
$\Rightarrow 50 \times g = V \times 10^{3} \times g$
$\Rightarrow V = \frac{1}{20} m^{3}$
The total volume of the ferry is $1 m^{3}$ , so the fraction which is immersed is $\frac{1}{20}$ .

$(b)$ Let due to leak, $m kg$ of fluid enters into the ferry such that it is about to immerse fully, i.e., the volume of water displaced at this condition is the total volume of the ferry, which is $1 m^{3}$ .
So, the weight of the displaced volume is balanced by the total weight of the ferry and the water inside it.
Hence, $\Rightarrow (m_{water} + m_{ferry}) \times g = V \times ρ_{w} \times g$
$\Rightarrow m_{water} + 50 = 1 \times 10^{3}$
$1 m^{3}$
The volume of this much water is, $V_{water} = \frac{m_{water}}{ρ_{water}}$
$= \frac{950}{10^{3}} m^{3}$
$= 0.95 m^{3}$
The fraction of volume of the water entered into the ferry to the volume of the ferry is $\frac{0.95}{1} = \frac{19}{20}$ .

Important Questions on Fluid Mechanics

Learn and Prepare for any exam you want !