Question

A solid sphere of volume V and density p, floats at the interface of two immiscible liquids of densities p1 and p2 respectively. If p1<p<p2, then the ratio of volume of the parts of the sphere in upper and lower liquids is?

Answer 1

let v is the the part of volume of sphere inside liquid having density p1, and V is the part dipped in liquid having density p2,
the weight of sphere = volume× density=
(v+V)pg. (g= acceleration due to gravity).
both the liquid contribute in balancing the weight of sphere. hence we can write,
v(p1)g+V(p2)g=(v+V)pg.
=> v(p1)+V(p2)= (v+V)p.
rearranging the above equation,
we get,
v(p1-p)=V(p-p2).
=> v/V=(p-p2)/(p1-p)

Answer 2

Heya...

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ANSWER FOR YOUR QUESTION IS HERE:

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let v is the the part of volume of sphere inside liquid having density p1, and V is the part dipped in liquid having density p2,

the weight of sphere = volume× density=

(v+V)pg. (g= acceleration due to gravity).

both the liquid contribute in balancing the weight of sphere. hence we can write,

v(p1)g+V(p2)g=(v+V)pg.

=> v(p1)+V(p2)= (v+V)p.

rearranging the above equation,

we get,

v(p1-p)=V(p-p2).

=> v/V=(p-p2)/(p1-p)

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