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The mass of a steamer is 10 tonnes. When...

The mass of a steamer is 10 tonnes. When it enters a fresh water lake from the sea, it displaces 50 L more water than before. Calculate the density of sea water. [Mass of 1L of fresh water = 1 kg]

Text Solution

Verified by Experts

Mass of displaced sea water = mass of the streamer
`=10xx10^(3)kg=10^(7)g`.
`therefore` Volume of displaced sea water
`=10^(7)/rhocm^(3)[rho="density of sea water"]`
Mass of displaced lake water = `10^(7)g`
As the density of fresh water is `1g*cm^(-3)`, the volume of displaced lake water = `10^(7)cm^(3)`.
According to the problem,
`10^(7)-10^(7)/rho=50xx10^(3)or,10^(7)(1-1/rho)=5xx10^(4)`
or, `1-1/rho=5/10^(3)or,1/rho=1-5/1000=95/1000`
`therefore" "rho=1000/995=1.005g*cm^(-3)`.
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