A ferry boat has internal volume `1m^3` and weight 50 kg. a. Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water. b. If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?

Answer

A, B

Explanation

`m=50kg`
`=v=1m^3`
=interN/Al volume
`=exterN/Al volume of the boat
a. Let `V_1rarr` volume of boat inside water =volume of water displaced in `m^3`. Since, weight of the boat is balanced by the buyoyant force
`rarr g=V_1xxrho_wxxg`
`rarr 50=V_1xx10^3`
`rarr v_1=5/100=0.05m^3`
b. `Let v_1rarr` volume of boat filed with water before water starts coming in from the side.
`:.mg+v^1rho_wxxg=Vxxrho_wxxg` [Boat must have displaced v amount of water]
`rarr 50+v^1xx10^3=1xx10^3`
`rarrv^1=(10^3-50)/10^3`
`=950/1000=0.95m^3`
`rarr Fraction of volume =19/20`