A ferry boat has internal volume `1m^3` and weight 50 kg. a. Neglecting the thickness of te wood, find the fraction of the volume of the boat immersed in water. b.If a leak develpops n 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`