KVPY SA Exam 2011 Question Paper

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 ${\mathrm{\rho }}_1$ as shown in the figure, the spring stretches by an amount ${\mathit{x}}_1\left(\mathit{\rho }>{\mathit{\rho }}_1\right)$. When the experiment is repeated in a liquid of density , the spring stretches by an amount ${\mathit{x}}_2$. Neglecting any buoyant force on the spring, the density of the object is