Fig. shows a small plane strip suspended from a fixed support through a string of length 1. A continuous beam of monochromatic light is incident horizontally on the strip and is completely absorbed. The energy falling on the strip per unit area per sec is P. The deflection of the string from the vertical, if the strip stays in equilibrium.

Options

A. `theta=sin^(-1)""(P)/(mgC)`
B. `theta=cos^(-1)""(P)/(mgC)`
C. `theta=tan^(-1)""(P)/(mgC)`
D. `theta=cot^(-1)""(P)/(mgC)`

Answer

C

Explanation

The liner momentum of the light failling per unit time on the strip is `(P)/(c)`. AS the light falls on the strip its momentum is aboserbed by it. The change in momentum imparated to the strip per unit time is thus `(P)/(C)`. This is equal to the force on the strip by the light beam. In equilibrium, the force by the light beam the wieght of the strip and force due to tension add to zero if the strip makes an angle `theta` vertical.
`T cos theta= mg`
Also `T sin theta=(P)/(c)`
Dividing we get, `tan theta=(P)/(mgc)`
`:. theta= "tan"^(-1)(P)/(mgc)`