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Question

In the arrangement as shown, A and B are two cylinders each of length L and density d1 and d2(d1<d2), respectively. They are joined together and submerged in the liquid of density d with length L/2 of A outside the liquid. If the difference in densities of two cylinders is equal to density of the liquid, find d1:

156910_19831bc9097d421d98d77e849fce2632.png

A
54d
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B
d4
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C
34d
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D
d2
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Solution

The correct option is A d4

Applying the law of flotation, we have weight of the two blocks = weight of water displaced by the blocks
Vd1g+Vd2g=Vdg+V2dg
d1+d2=32d ......... (I)
d2d1=d ......... (II) given
(I)(II) gives
2d1=d2d1=d4


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