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A sample of a metal weighs $70 g m$ in air, $60 g m$ in water and $40 g m$ in a liquid. Then which of the following statements are correct

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Specific gravity of the liquid is $\frac{1}{7}$

Specific gravity of the liquid is $3$

Specific gravity of the metal is $3$

Specific gravity of the metal is $7$

answer is B, C.

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Detailed Solution

$m g = 70 g$

$m g (1 - \frac{ρ_{w}}{ρ}) = 60 g$

$\Rightarrow 1 - \frac{ρ_{w}}{ρ} = \frac{6}{7}$ $\Rightarrow \frac{ρ_{w}}{ρ} = \frac{1}{7}$ $\Rightarrow \frac{ρ}{ρ_{w}} = 7$

$ρ = 7 ρ_{w}$

$m g (1 - \frac{ρ_{l}}{7 ρ_{w}}) = 40 g \Rightarrow 1 - \frac{ρ_{l}}{7 ρ w} = \frac{4}{7} \Rightarrow \frac{ρ_{l}}{ρ_{w}} = 3$

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