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In a cylindrical container water is fill...


In a cylindrical container water is filled up to a height of `h_(0)=1.0m`. Now a large number of small iron balls are gently dropped one by one into the container till the upper layer of the balls touches the water surface. if average density of the contents is `rho=4070 kg//m^(3)`, density of iron is `rho_(i)=7140kg//m^(3)` and density of iron is `rho_(0)=1000kg//m^(3)` find the height `h` of the water level (in S.I. units) in the container with the iron balls.

Text Solution

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The correct Answer is:
2
`rho=("total mass")/("total volume")=(m_(1)+m_(2))/(Ah)`
`rho_(0)=(m_(1))/(Ah_(0)),rho_(i)=(m_(2))/(A(h-h_(0)))`
`impliesh=(rho_(0)h_(0)+(h+h_(0))rho_(i))/(rho)=((rho_(i)-rho_(0)))/((rho_(i)-rho))=2m`
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