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Volume of a sphere

A vertical U-...

Question

A vertical U-tube of uniform cross-section contains mercury in both sides of its arms as shown below. Gylcerine column of $10 c m$ is introduced into one of its arms. Oil of density $0.8 g / c c$ is poured into the other arm until the upper surface of the oil and glycerine are at same horizontal level. [ $ρ_{H g} = 13.6 g / c c, ρ_{g l y c e r i n e} = 1.3 g / c c$ ] The length of oil column is

A

10.4 c m

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B

8.2 c m

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C

7.2 c m

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D

9.6 c m

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Solution

The correct option is D $9.6 c m$
$0.8 \times L + 13.6 (10 - L) = 1.3 \times 10$

$0.8 L + 136 - 13.6 L = 13$

$12.8 L = 123$

$L = 9.6 c m$

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