Figure shows a small, plane strip suspended from a fixed support through a string of length l. A continuous beam of monochromati clight is incident horizontally on the strip and is completely absorbed. The energy falling on the strip per unit time is W. (a) Find the deflection of the string from the vertical if the mirror stays in equilibrium. (b) If the strip is deflected slightly from its equilibrium position in the plane of the figure, what will be the time period of the resulting oscillations?

Explanation

(a) The linear momentum of the light falling per unit time on the strip is W/c. As the light is incident on the strip, its momentum is absorbed by the mirror. The change in momentum imparted to the strip per unit time is thus W/c. This is equal to the force on the strip by the light beam, the weight of the strip and the force due to tension add to zero. If the string makes an angle theta with the vertical,
T cos theta = mg
` and T sin theta = W/c`.
Thus, `tan(theta) = (W/ mgc).`
(b) In equilibrium, the tension is
` T= ([(mg)^2 + (W/c)^2]^(1/2))`
` or, T/m = ([(g^2)+(W/mc)^2]^(1/2)). `
This plays the role of effective g. The time period of
small oscillations is
` t=(2pi (sqrt(l/(t//m))))= 2 pi ((sqrt l)/([ (g^2) + (W/mc)^2]^1/4).`