A metal sphere weighing $60 g m$ in the air is suspended by a thread in oil of specific gravity $0.6$ . If the tension in the thread is 55gmwt, the specific gravity of the metal sphere is

9.4

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4.5

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6.3

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7.2

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Solution

The correct option is D $7.2$
Given,

Weight of metal sphere in air, $w_{1} = 60 g m$

Weight of metal sphere in oil, $w_{3} = 55 g m$

Specific gravity in oil $= 0.6$

Relative density at specific gravity $= \frac{w_{1} - w_{3}}{w_{1} - w_{2}}$

$⟹ 0.6 = \frac{60 - 55}{60 - w_{2}}$

$0.6 (60 - w_{2}) = 60 - 55$

$60 - w_{2} = 60 - 55$

$60 - w_{2} = \frac{5}{0.6}$

$60 - \frac{5}{0.6} = w_{2}$

$\frac{31}{0.6} = w_{2}$

$w_{2} = 51.6$

Specific gravity in air $= \frac{w_{1}}{w_{1} - w_{2}}$

$= \frac{60}{60 - 51.6}$

$= \frac{60}{8.4} = 7.2$

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