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Question

A boat having a length of 3m and a breadth of 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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Solution

Step1: Given data

The boat has a length of 3 m and a breadth of 2 m and sinks by 1cm when the man gets on it.

Step2: Formula used

Whenever an object has some of its volume inside the water, this object will experience an upward force called buoyant force which is given by the formula,

Fb=ρwvg

[ where ρw=density of water, g=acceleration due to gravity, v=volume of the object that is inside the water. ]

Step3: Calculating volume

l=3m,b=2m,h=1cm=0.01m

v=l×b×h[v=volume,l=length,b=breadth,h=height]v=3×2×0.01v=0.06m3

Step4: Calculating buoyant force experienced by the boat

Density of water ρw-100kg/m3

Now we'll substitute the value of volume and density in the buoyant force formula

Fb=ρwvg=1000×0.06×gFb=60g..........(i)

Step5: Calculating the mass of the man

Let us assume the mass of the man is m kg.
Since man is inside the boat, the boat will experience a downward force. This downward force is equal to,

F=mg.................(ii)

Since the boat is in equilibrium, we can equate the upward force in equation (i) and the downward force in equation (ii).

So, we get,

60g=mgm=60kg

Hence, the mass of the man is 60kg.


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