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A spider is hanging by means of its own ...

A spider is hanging by means of its own silk thread directly above a transparent fixed sphere of radius `R=20cm` as shown in the figure. The refractive index of the material of the sphere is equal to `sqrt(2)` and the height of the spider from the centre of the sphere is `2R(=40cm)`. An insect, initially sitting at the bottom, starts crawling on the sphere along a vertical circular path with the constant speed of `pi//4 cm//s`. For how long time the insect will be invisible for the spider, assume that it crawls once round the vertical circle.

A

`80 sec`

B

`(320)/(3)sec`

C

`(160)/(3)sec`

D

`(80)/(3)sec`

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