JEE Main 2026 — 22 January, Morning Shift — Question 29

$\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\sqrt{\frac{2 \mathrm{G} \times \rho \times \frac{4 \pi \mathrm{R}^{3}}{3}}{\mathrm{R}}} \Rightarrow \mathrm{V}_{\mathrm{e}} \propto \sqrt{\rho} \times \mathrm{R}$ $\frac{\left(\mathrm{V}_{\mathrm{e}}\right)_{\mathrm{B}}}{\left(\mathrm{V}_{\mathrm{e}}\right)_{\mathrm{A}}}=\sqrt{\frac{\rho_{\mathrm{B}}}{\rho_{\mathrm{A}}}} \times \frac{\mathrm{R}_{\mathrm{B}}}{\mathrm{R}_{\mathrm{A}}}=\sqrt{\frac{0.1 \rho_{\mathrm{A}}}{\rho_{\mathrm{A}}}} \times\left(\frac{0.1 \mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{A}}}\right)$ $\frac{\left(\mathrm{V}_{\mathrm{e}}\right)_{\mathrm{B}}}{\left(\mathrm{V}_{\mathrm{e}}\right)_{\mathrm{A}}}=\frac{1}{10} \times \frac{1}{\sqrt{10}}$ $\left(\mathrm{V}_{\mathrm{e}}\right)_{\mathrm{B}}=\frac{10 \times 1000}{10 \sqrt{10}}=100 \sqrt{10} \mathrm{~m} / \mathrm{sec}$