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An ice cube is floating in water above w...

An ice cube is floating in water above which a layer of a fighter oil is poured. As the ice melts completely, the level If water surface (or interface) and upper level of oil will

A

rise and fall

B

fall and rise

C

not change and no change

D

not change and fall

Text Solution

Verified by Experts

The correct Answer is:
A
When ice melts into water its volume decrease. Hence, over all level should decrease.
Now suppose m is the mass of ice `(V_1)` is volume immersed in water and `(V_2)` the volume immersed in oil. Then in floating condition,
weight=upthrust
`:. mg=(V_1)(rho_w)g+(V_2)(rho_0)g`
`:. (V_1)=(m-(V_2)(rho_0))/(rho_w)`
`(m)/(rho_w)-(V_(2)(rho_0))/(rho_w)` ...(i)
When ice melts, m mass of ice converts into m mass of water. Volume of water so formed is
`V_(3)=(m)/(rho_(w))` ...(ii)
From Eqs. (i) and (ii) ,`V_(3)gtV_(1)`
`:.` Interface level will rise.
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