To determine the composition of a bimetalic alloy, a sample is first weighed in air and then in water. These weights are found to be w_(1)andw_(2) respectively. If the densities of the two constituent metals are p_(1)andp_(2) respectively, then the weight of the first metal in the sample is (where rho_(w) is the density of water)

To determine the composition of a bimetalic alloy, a sample is first w

1.	To determine the composition of a bimetalic alloy, a sample is first weighed in air and then in water. These weights are found to be w_(1)andw_(2) respectively. If the densities of the two constituent metals are p_(1)andp_(2) respectively, then the weight of the first metal in the sample is (where rho_(w) is the density of water)
Answer» `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)-rho_(w))-w_(2)rho_(2)]` `rho_(1)/(rho_(w)(rho_(2)+rho_(1)))[w_(1)(rho_(2)-rho_(w))+w_(2)rho_(2)]` `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)+rho_(w))-w_(2)rho_(1)]` `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)-rho_(w))-w_(2)rho_(1)]` Solution :`w_(1)-w_(2)=Vrho_(w)g=(V_(1)+V_(2))rho_(w)g=[X/rho_(1)+(w_(1)-x)/rho_(2)]rho_(w)` Hence, required weight, `x=rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)-rho_(w))-w_(2)rho_(2)]`