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A ball of volume V and density rho(1) is...

A ball of volume V and density `rho_(1)` is moved downwards by a distance 'd' in liquid of density `rho_(2)`. Find total change in potential energy of the system.

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The correct Answer is:
A, B, D
Decrease in potential energy of the ball.
`=m_(1)gh (m_(1)=`mass of ball)
`=(V_(rho_(1)))gd`
or, `Delta U_(1)=-V_(rho_(1))gd`
When `V`volume of solid comes down, then it is replaced by `V` volume of liquid.
` :.` Increase in potential energy of liquid:
`= m_(2)gh (m_(2)=`mass of liquid of volume `V)`
`=(V_(rho_2))gd`
or, `:. Delta U_(2)=-V_(rho_(2))gd`
Total change in potential energy.
`Delta U =Delta U_(1) +Delta U_(2)=V(rho_(2)-(rho_(1)) gd`.
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