1.

A trough contains the two immiscible liquids 'A' and 'B' having densities 'p_(A)'and'p_(B)'(p_(B)gtp_(A)). A cylindrical body having uniform area of cross section is immersed completely and vertically in the liquids such that 1//3rd of its length is in liquid 'B' and the remaining is in liquid 'A'. Find the density of the body.

Answer»

Solution :Take the volume of cylindrical body as V.
Is the cylindrical body completely immersed in both immiscible liquids 'A' and 'B' ?
Find the volume of the cylinder immersed in liquid 'A' and also in liquid 'B' by using FORMULA,
V=a.h(1)
Is this equal to the volume of the DISPLACED liquids of 'A' (or) 'B' ?
Now, weight of floating body = weight of the displaced liquids = total UPTHRUST acting on the body.
Here, weight of floating body = mg
= `Vd_(s)g`(2)
`rArr"Then",V.d_(s)g=(2)/(3)V*d_(Axx)g+(1)/(3)Vd_(B)g`(3) Find the DENSITY of the body from equation (3)


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