The question is: A small laser emits light at power 5.00mW and wavelength 633nm.

Question

The question is:

A small laser emits light at power 5.00mW and wavelength 633nm. The laser beam is focused until its diameter matches the 1266nm diameter of a sphere placed in its path. The sphere is perfectly absorbing and has density 5 x 103 kg/m3. What is the magnitude of the corresponding force and the magnitude of the acceleration that force alone would givethe sphere?

So i get the force is equal to 1.67 x 10-11, which is correct. What i don't get is how to calculate the acceleration? I calculate the mass of the sphere by using the m =d x V. Isn't the equation for Volume of a sphere 4/3(pi)r2, but the textbook use (pi)(r2) only?  

Explanation / Answer

given,

power = 50 mW

wavelength = 633 nm

diameter = 1266 * 10^-9 m

density = 5 * 10^3 kg/m^3

force = power / speed of light

force = 5 * 10^-3 / 3 * 10^8

force = 1.67 * 10^-11 N

volume of the sphere = 4/3 * pi * r^3

volume of the sphere = 4/3 * pi * (1266 * 10^-9 / 2)^3

mass = density * volume

mass = 5 * 10^3 * 4/3 * pi * (1266 * 10^-9 / 2)^3

mass = 5.312 * 10^-15 kg

force = mass * acceleration

1.67 * 10^-11 =  5.312 * 10^-15 * acceleration

acceleration = 3143 m/s^2

acceleration that force alone would givethe sphere = 3143 m/s^2

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