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A boat having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1cm...

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spsaroj | Student, Grade 10 | (Level 2) Honors

Posted June 5, 2013 at 6:20 AM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 5, 2013 at 6:45 AM (Answer #1)

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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. This gives the mass of the man as 0.06*1000 = 60 kg. The man has a mass of 60 kg.

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