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Question

A slender homogenous rod of length 2L floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75. The length of rod that extends out of water is?
1164189_870682f5ee3a4debbe3ca1c86b7c1994.png

A
L
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B
12L
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C
14L
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D
3L
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Solution

The correct option is B 12L
let h be height of rod inside water. A = area of cross section.
d = density of rod, dw density of water
mass of rod = mass of water displaced
d×A×2L=dw×h×A
h=2L×ddw=2L×0.75=3L2
Height of rod outside the water =L2

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