High School

We appreciate your visit to A boat with a length of 3 meters and a breadth of 2 meters is floating on a lake The boat sinks by 1 cm. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A boat with a length of 3 meters and a breadth of 2 meters is floating on a lake. The boat sinks by 1 cm when a man gets on it. What is the mass of the man?

Answer :

Final answer:

The mass of the man can be found by calculating the volume of water the boat displaces when he steps onto it and sinks by 1 cm, and using the density of water to convert this volume into mass. Hence, the mass of the man is 60 kg.

Explanation:

To determine the mass of the man who causes a boat to sink by 1 cm when he gets on it, we can use the principle of buoyancy, specifically Archimedes' Principle. The principle states that the upward buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by the body's volume. When the man steps on the boat, the boat sinks, displacing more water until the additional buoyant force equals the man's weight.

First, we calculate the volume of water displaced by the boat when it sinks by 1 cm due to the man's weight:
Length of the boat, L = 3 m
Breadth of the boat, B = 2 m

Distance the boat sinks, h = 1 cm = 0.01 m

Volume of water displaced (V) = L ×B × h

V = 3 m × 2 m ×0.01 m

V = 0.06 m3

The density of water (hopw) is approximately 1000 kg/m3. Using the formula for the mass of the displaced water (mw), which is equal to the density of water multiplied by the volume displaced, we get:

mw = hopw × V

mw = 1000 kg/m3 × 0.06 m3

mw = 60 kg

Therefore, the mass of the man is 60 kg.

Thanks for taking the time to read A boat with a length of 3 meters and a breadth of 2 meters is floating on a lake The boat sinks by 1 cm. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada