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

1. A \(\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)-w_{2} \rho_{2}\right]\)
2. B \(\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}+\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)+w_{2} \rho_{2}\right]\)
3. C \(\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}+\rho_{w}\right)-w_{2} \rho_{1}\right]\)
4. D \(\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{1}-\rho_{w}\right)-w_{z} \rho_{1}\right]\)