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Question: The fraction of a floating object of volume \(V _ { 0 }\) and density \(d _ { 0 }\) above the surfac...

The fraction of a floating object of volume V0V _ { 0 } and density d0d _ { 0 } above the surface of a liquid of density d will be

A

d0d\frac { d _ { 0 } } { d }

B

dd0d+d0\frac { d d _ { 0 } } { d + d _ { 0 } }

C

d−d0d\frac { d - d _ { 0 } } { d }

D

dd0d−d0\frac { d d _ { 0 } } { d - d _ { 0 } }

Answer

d−d0d\frac { d - d _ { 0 } } { d }

Explanation

Solution

For the floatation ⇒

∴ Vout =V0−Vin =V0−V0d0dV _ { \text {out } } = V _ { 0 } - V _ { \text {in } } = V _ { 0 } - V _ { 0 } \frac { d _ { 0 } } { d } =V0[d−d0d]= V _ { 0 } \left[ \frac { d - d _ { 0 } } { d } \right]

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