A piece of an alloy of mass 96 gm is composed of two metals whose specific gravities are 11.4 and 7.4. if the weight of the alloy is 86 gm in water, find the mass of each metal in alloy.

Explanation

Suppose the mass of the metal of specific gravity `11.4` be m and the mass of the second metal of specific gravity `7.4` will be (96–m)
Volume of first metal`=(m)/(11.4) cm^(3)`
Volume of second metal`=(96-m)/(7.4) cm^(3)`
Total volume `=(m)/(11.4)+(96-m)/(7.4)`
Buoyancy force in water `=((m)/(11.4)+(96-m)/(7.4))`gm
weight
Apparent wt. in water
=`96--[((m)/(11.4))+((96-m))/(7.4))]=86`
or `" "(m)/(11.4)+((96-m))/(7.4)=10`
Solvings we get, `" "m=62.7`gm
Thus mass of second metal is `=96-62.7=33.3` gm