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Question

Figure shows a metal ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has height 6 cm, face area 11cm2 on the top and bottom and density 0.5g/cm3,4cm of cylinder's height is inside the water surface. If density of the metal ball is 8gm/cm3 then its radius is equal to (3x)1/3 cm. calculate x. (ρw=1gm/cm3)
1501216_fa405972156d4328a776cb3a70d0b5f3.png

A
7
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B
5
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C
3
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D
8
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Solution

The correct option is D 8
In the given figure.
8×(43πR3)×g+0.5(6×11)×g=1[43πR3+4×11]g

7[43πR3]g=11g

R3=11×328π

R=(11×328π)1/3

x=28π118
Hence,
option (D) is correct answer.

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