Question

A boat having a length 3m and breadth 2m is floating on a lake.The boatsinks by 1 cm when a man gets into it.The mass of the man is:

• A. 50kg
• B. 60kg
• C. 70kg
• D. 80kg

Answer 1

Answer:

B. 60kg

Use the principle of flotation:

When the man gets into the boat, the boat sinks an additional 1 cm = 0.01 m. The extra volume of water displaced equals the volume submerged due to the man's weight.

Extra displaced volume:

$V = \text{length} \times \text{breadth} \times \text{additional depth}$
$V = 3 \times 2 \times 0.01 = 0.06 , \text{m}^3$
The mass of water displaced is:

$m = \rho V$

where the density of water $(\rho = 1000 , \text{kg/m}^3).$

$m = 1000 \times 0.06 = 60 , \text{kg}$

Since the weight of the displaced water equals the weight of the man,

$\boxed{\text{Mass of the man} = 60 \text{ kg}}$

Answer: $(\boxed{60\ \text{kg}})$.