In a region of space where gravitational forces can be neglected, a sphere is accelerated by a uniform light beam of intensity 8.0 mW/m^2. The sphere is totally absorbing and has a radius of 1.0 microns and a uniform density of 4500.0 kg/m^3. What is the magnitude of the sphere's acceleration (in m/s^2) due to the light? A. 5.0x10^-26B. 4.4x10^-9C. 1.5*10^-9D. 9.8x10^-8E. 3.0x10^-15

The correct answer is B

Explanation:

To calculate the acceleration we must use Newton's second law

F = m a

a = F / m

To calculate the force we use the defined pressure and the radiation pressure for an absorbent surface

P = I / c absorbent surface

P = F / A

F / A = I / c

F = I A / c

The area of area of a circle is

A = π r²

We replace

F = I π r² / c

Let's calculate

F = 8.0 10⁻³ π (1.0 10⁻⁶) ²/3 10⁸

F = 8.375 10⁻²³ N

Density is

ρ = m / V

m = ρ V

m = ρ (4/3 π r³)

m = 4500 (4/3 π (1 10⁻⁶) ³)

m = 1,885 10⁻¹⁴ kg

Let's calculate the acceleration

a = 8.375 10⁻²³ / 1.885 10⁻¹⁴

a = 4.44 10⁻⁹ m/s² absorbent surface

The correct answer is B