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27 April, 23:34

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

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  1. 28 April, 00:02
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    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
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