A solid of relative density 1.25 is found to weigh 12 g in water. Find its weight in air.

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Solution

$T_{o b j e c t} = 1.25 g / c m^{3} W_{w a t e r} = 12 g W_{a i r} = T_{o b j e c t} V g W_{w a t e r} = T_{o b j e c t} V g - T_{w a t e r} V g W_{w a t e r} = W_{a i r} - T_{w a t e r} V g W_{a i r} = W_{w a t e r} + T_{w} V g = 12 + (1 \times \frac{W_{a i r}}{T_{o b j e c t}}) W_{a i r} = 12 + \frac{W_{a i r}}{1.25} \Rightarrow 1.25 W_{a i r} = W_{a i r} + 15 \Rightarrow \frac{1}{4} W_{a i r} = 15 \Rightarrow W_{a i r} = 60 g$ .

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