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A thin plane strip is suspended from a fixed support through a string of length l. Material of the strip is such that is absorbs all the light falling on it. A parallel beam of light with power P moving horizontally is striking the plane strip . Find the angle made by string with the vertical if strip remains in equilibrium . If strip is slightly disturbed from its equilibrium position and then released , its equilibrium position and then released , what will be time period of resulting oscillation ? |
Answer» Solution :If light of power P is falling normally on perfectly absorbing surface , then force applied bythe light beam on surface is P/C and in this case , the force is ACTING along horizontal direction as shown in figure.  Let `theta` be the angle made by string with the VERTICAL when in equilibrium , then we can write the following equation: ` T cos theta = MG ` `T sin theta = P/c` To find the angle `theta` , we can divide the above two equations as follows : `tan theta=P/(mgc)impliestheta=tan^(-1)(p/(mgc))` Tension of the string can be written as follows : `T=sqrt(((P)/(c))^2+(mg)^2)` Hence EFFECTIVE gravity can be written as follows : `g. =T/m=sqrt((P/(mc))^2+g^2)` Time period of oscillation can be written as follows: Time period `2pisqrt(l/(g.))` `implies` Time period `=2pisqrt(l/(sqrt((P/(mc))^2)+g^2))` |
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