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_(1)x_(1)-rho_(2)x_(2))/(x_(1)-x_(2))`
B. `rho=(rho_(1)x_(2)-rho_(2)x_(1))/(x_(2)-x_(1))`
C. `rho=(rho_(1)x_(2)+rho_(2)x_(1))/(x_(2)+x_(1))`
D. `rho=(rho_(1)x_(2)+rho_(2)x_(1))/(x_(1)+x_(2))`

Answer

B