In the figure, a laser beam of power 4.60 W and diameter 2.50 mm is directed upw

Question

In the figure, a laser beam of power 4.60 W and diameter 2.50 mm is directed upward at one circular face (of diameter less than 2.50 mm) of a perfectly reflecting cylinder, which is made to "hover" by the beam's radiation pressure. The cylinder's density is 2.10 g/cm3. What is the cylinder's height H? (mm)

Please show all work and explain your methods. I have tried these six answers

1) 1.24x10^10 mm 2 Incorrect. (Try 2) 1.24x10^-6 m 3 Incorrect. (Try 3) 0.00124 m 4 Incorrect. (Try 4) 7.59x10^-7 mm 5 Incorrect. (Try 5) 7.59x10^-10 mm 6 Incorrect. (Try 6) 7.59x10^-10 m

Explanation / Answer

As

F = P / c

Then

F = 1.534E-8 N

As

F = m g

and

m = D V

Then

F = D V g

as

V = pi r^2 H

Then

F = pi D r^2 H g

Thus,

H = F / [pi D r^2 g]

Then,

H = 1.519*10^-7 m   [ANSWER]

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