$=\frac{\mathrm{dF} / \mathrm{A}}{\mathrm{dx}}=\frac{(\mathrm{dm}) \mathrm{a} / \mathrm{A}}{\mathrm{dx}}=\frac{(\rho \cdot \mathrm{d}(\mathrm{vol} .)) \mathrm{a}}{\mathrm{A} \,\mathrm{dx}}$

$\tan \theta=\rho a$

$\frac{\tan 37^{\circ}}{\tan 53^{\circ}}=\frac{\rho_{1}}{\rho_{2}}=\frac{9}{\rho_{2}}$

$\Rightarrow \rho_{2}=16 \mathrm{gm} / \mathrm{cm}^{3}$