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A ball of mass m and density rho is imme...

A ball of mass m and density `rho` is immersed in a liquid of density `3 rho` at a depth `h` and released. To what height will the ball jump up above the surface of liqud ? (neglect the reistance of water and air).

Text Solution

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Volume of ball `V=m/(rho)`
Acceleration of ball inside the liquid
`a=(F_("net"))/m=("upthrust "-"weight")/m`
`a=((m/(rho))(3rho)(g)-mg)/m=2g` (upwards)
`:.` velocity of ball while reaching at surface
`V=sqrt(2ah)=sqrt(4gh)`
`:.` The ball will jump to a height
`H=(v^(2))/(2g)=(4gh)/(2g)=2h`
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