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A boat with a length of $3 m$ and a breadth of $2 m$ is floating. When a man gets on it, the boat sinks in the water by $1 cm$ . The mass of the man in $kg$ will be

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60 kg

72 kg

12 kg

18 kg

answer is A.

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Detailed Solution

A boat with a length of

3 m

and a breadth of

2 m

is floating. When a man gets on it, the boat sinks in the water by

1 cm

. The mass of the men will be

60 kg

.
Given,
Length of the boat,

l = 3 m

Breadth of the boat,

b = 2 m

Depth of the boat sink,

h = 1 cm

= 1 0^{- 2}

m
When a man gets into the boat it sinks

1 cm

, so the total water replaced by that boat will be equal to the volume of the boat (V) immersed in water which can be calculated by the formula,

V = l \times b \times h

= 3 \times 2 \times 1 \times 10^{- 2} m^{3}

= 6 \times 10^{- 2} m^{3}

Density of water is

1000 kg / m^{3}

so the man will displace the water equivalent to his mass
So, the mass of the man will be
Mass of man

=

volume of water displaced

\times

density of water

= 1000 \times 6 \times 10^{- 2}

= 60 kg

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