A boat having a length 3m and breadth 2 meter is floating on a lake . the boat sinks by 1 cm, when a man gets into it. the mass of the man is?
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L=3m, B= 2m, h=1cm= .01m
Vol of water displaced= 3 × 2×.01
vol of water displaced = 0.06m^3
mass = vol × density
density of water= 1000 kg/m^3
mass of man = 0.06 × 1000
mass of man = 60 kg
Vol of water displaced= 3 × 2×.01
vol of water displaced = 0.06m^3
mass = vol × density
density of water= 1000 kg/m^3
mass of man = 0.06 × 1000
mass of man = 60 kg
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Answer:
The mass of the man is 60 kg.
Explanation:
The buoyant force experienced by the boat is calculated as,
(1)
Where,
=buoyant force acting on the boat
ρ=density of water=1000kg/m³
V=volume of the boat
g= acceleration due to gravity=10m/s²
From the question we have,
The length of the boat(l)=3m
The breadth of the boat(b)=2m
The height to which the boat sinks(h)=1cm=0.01m
The Volume is calculated as,
(2)
By putting the values in equation (2) we get;
(3)
By putting all the values in equation (1) we get;
(4)
The buoyant force is calculated as,
(5)
m=mass of the man
By equating equations (4) and (5) we get;
Hence, the mass of the man is 60 kg.
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