Indian Navy SSR (Sailor) Physics — practice by topic

**Critical angle formula** (denser → rarer): $\sin C = \dfrac{\mu_{\text{rarer}}}{\mu_{\text{denser}}} = \dfrac{1}{\mu_{\text{denser}}} = \dfrac{1}{1.5} \approx 0.667$. $C = \sin^{-1}(0.667) \approx 41.8° \approx 42°$. **Why option C (60°) is tempting.** Some recall $\sin^{-1}(0.866) = 60°$ — but that's $\mu = 1/0.866 \approx 1.15$, not $1.5$. **A useful sanity check:** as $\mu$ rises, the critical angle drops (denser glass holds light in more aggressively). Diamond's $C \approx 24°$ — that's why it sparkles.

Ohm's law: $V = IR$, where $R$ is constant for an ohmic conductor at fixed temperature. So $V$ is *directly proportional* to $I$ — the V–I graph is a straight line through the origin with slope $R$. For non-ohmic conductors (diodes, transistors), $R$ depends on $V$ or $I$, and the graph isn't a straight line.

Escape velocity from Earth's surface: $v_e = \sqrt{2gR}$ (using the surface relation $GM/R^2 = g$). $v_e = \sqrt{2 \times 9.8 \times 6.4 \times 10^6} = \sqrt{1.25 \times 10^8} \approx 1.12 \times 10^4$ m/s $= 11.2$ km/s. Option A ($7.9$ km/s) is the *orbital* velocity at Earth's surface, smaller by a factor of $\sqrt{2}$. That trap is identical to the one in the orbital-velocity question.