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Question

# A sphere of radius 1.00 cm is placed in the path of a parallel beam of light of large aperture. The intensity of the light is 0.50 W/cm2. If the sphere partially absorbs (α=0.25) the radiation falling on it, find the force exerted by the light beam on the sphere.

A
5.2×107 N
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B
9.16×109 N
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C
8.5×107 N
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D
9.3×107 N
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Solution

## The correct option is B 9.16×10−9 NForce=IAc(1+r)=πr2Ic(1+r) Given, I=0.5 W/cm2=5000 W/m2 r=1 cm=10−2 m, c=3×108 m/s α=0.25⇒r=1−α=1−0.25=0.75 ⇒F=π×(10−2)2×50003×108×(1+0.75) ∴F=9.16×10−9 N Hence, (C) is the correct answer. Why this question? Caution: If α is given in the question, we can use the formula, Force=IA(2−α)c Else, calculate, r=1−α for using the formula used in solution.

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