Question

A boat having a length of 3 and breadth 2 metre is floating on a lake. the boat sinks by one cm when a man gets own it. the mass of the man is?

Answer 1

The boat has a length of 3 m and the breadth is 2 m. The area of cross-section is 3*2 = 6 m^2. When the man gets on the boat it sinks by 1 cm.

The boat is floating in a lake filled with water. The buoyant force generated when the boat sinks by m meters is equal to the weight of water displaced.
For equilibrium this has to be equal to the weight of the man that gets into the boat.
The volume of water displaced is 6*0.01 = 0.06 m^3.
The density of water is 1000 kg/m^3.
We know density =Mass/Volume.
This gives the mass of the man as 0.06*1000 = 60 kg.
The man has a mass of 60 kg.

Hope this helps :)