Question

A mango tree is at the bank of a river and one of the branch of tree extends over the river. A tortoise lives in the river. A mango falls just above the tortoise. The acceleration of the mango falling from tree as it appears to the tortoise is (refractive index of water is $4/3$ and the tortoise is stationary).

• A. $g$
• B. $3g/4$
• C. $4g/3$
• D. None of these

Answer 1

The correct option is C $4g/3$

Let u be the actual distance of mango from the water surface and v be the distance of it as observed by tortoise due to refraction inside water.

Using the relation $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

Here since the surface is plane, $R=\infty$

Therefore, $v=\frac{4}{3}u$

$\frac{d^{2}v}{d{t}^2}=\frac{4}{3}\frac{d^{2}u}{d{t}^2}$

Therefore acceleration as seen by tortoise=$\frac{d^{2}v}{d{t}^2}=\frac{4}{3}g$