An object with uniform density ρ is attached to a spring that is known to stretch linearly with applied force as shown below.
When the spring-object system is immersed in a liquid of density `rho_(1)` as shown in the figure, the spring stretches by an amount `x_(1)(rho gt rho_(1))`. When the experiment is repeated in a liquid of density `rho_(2) gt rho_(1)`, the spring stretches by an amount `x_(2)`. Neglecting any buoyant force on the spring, the density of the object is

Options

A. `rho=(rho_1x_1-rho_2x_2)/(x_1-x_2)`
B. `rho=(rho_1x_2-rho_2x_1)/(x_2-x_1)`
C. `rho=(rho_1x_2+rho_2x_1)/(x_1+x_2)`
D. `rho=(rho_1x_1+rho_2x_2)/(x_1+x_2)`