JEE Physics 2026 Question with Solution

Step-by-step solution

Common mistakes

• Using $v_e \propto \sqrt{R^2\rho}$ and then simplifying it incorrectly as a direct factor of $0.1$. This is wrong because $\sqrt{R^2\rho} = R\sqrt{\rho}$, so both the radius factor and the square root of density must be handled separately. Instead, use $\frac{v_B}{v_A} = 0.1\sqrt{0.1}$.

• Forgetting to convert $10 \, \text{km/s}$ into $\text{m/s}$ before comparing with the options. This is wrong because the final answer is asked in $\text{m/s}$. Convert first: $10 \, \text{km/s} = 10^4 \, \text{m/s}$.

• Assuming escape velocity depends only on density or only on radius. This is wrong because after substituting $M = \frac{4}{3}\pi R^3\rho$ into $v_e = \sqrt{\frac{2GM}{R}}$, the dependence becomes $v_e \propto R\sqrt{\rho}$. Both quantities affect the result.