Rod of constant cross-section moves towards right with constant acceleration. Graph of stress and distance from left end is given as in figure. If density of material of rod at cross section $1$ is $9$ $\frac{{gm}}{{c{m^3}}}$ . Find density at cross section $2$.
.......... $\mathrm{gm} / \mathrm{cm}^{3}$
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$\tan \theta=\frac{\mathrm{d}(\text { stress })}{dx}(\text { slope })$
$=\frac{\mathrm{dF} / \mathrm{A}}{\mathrm{dx}}=\frac{(\mathrm{dm}) \mathrm{a} / \mathrm{A}}{\mathrm{dx}}=\frac{(\rho \cdot \mathrm{d}(\mathrm{vol} .)) \mathrm{a}}{\mathrm{A} \,\mathrm{dx}}$
$\tan \theta=\rho a$
$\frac{\tan 37^{\circ}}{\tan 53^{\circ}}=\frac{\rho_{1}}{\rho_{2}}=\frac{9}{\rho_{2}}$
$\Rightarrow \rho_{2}=16 \mathrm{gm} / \mathrm{cm}^{3}$
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