Question

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?

Answer 1

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

Answer 2

Answer:

The mass of the man is 60 kg.

Explanation:

The buoyant force experienced by the boat is calculated as,

$F_b=\rho Vg$     (1)

Where,

$F_b$=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,

$V=l\times b\times h$                   (2)

By putting the values in equation (2) we get;

$V=3\times 2\times 0.01$

$V=0.06m^3$          (3)

By putting all the values in equation (1) we get;

$F_b=1000\times 0.06\times 10$

$F_b=600N$   (4)

The buoyant force is calculated as,

$F_b=mg$      (5)

m=mass of the man

By equating equations (4) and (5) we get;

$mg=600$

$m\times 10=600$

$m=60kg$

Hence, the mass of the man is 60 kg.

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