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

The correct option is C 9.16×109 N
Force=IAc(1+r)=πr2Ic(1+r)

Given, I=0.5 W/cm2=5000 W/m2
r=1 cm=102 m, c=3×108 m/s
α=0.25r=1α=10.25=0.75

F=π×(102)2×50003×108×(1+0.75)

F=9.16×109 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(2α)c

Else, calculate, r=1α for using the formula used in solution.

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