question_answer

A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is \[2\pi /\omega \] and the fish is 12 cm below the water surface, the radius of this circle in cm is

A)  \[\pi /\omega \]                             

B)  \[\frac{4}{3}\]                  

C)  \[36\sqrt{7}\]                  

D)        \[\frac{36}{\sqrt{7}}\]

Correct Answer: B

Solution :

The situation is shown in figure. \[\frac{G{{m}_{1}}{{m}_{2}}}{r}=\frac{1}{2}{{m}_{1}}v_{1}^{2}+\frac{1}{2}{{m}_{2}}v_{2}^{2}\] \[\Rightarrow \] \[\frac{m_{1}^{2}v_{1}^{2}}{{{m}_{1}}}+\frac{m_{2}^{2}v_{2}^{2}}{{{m}_{2}}}=\frac{2G{{m}_{1}}{{m}_{2}}}{r}\]   \[{{v}_{1}}=\sqrt{\frac{2GM_{2}^{2}}{r({{m}_{1}}+{{m}_{2}})}}\] or  \[{{v}_{2}}=\sqrt{\frac{2Gm_{1}^{2}}{r({{m}_{1}}+{{m}_{2}})}}\] \[\therefore \]