Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quasar. Express

Question

Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quasar. Express your answer using two significant figures.2.) A 6 MSun black hole that formed in the supernova of a massive star. Express your answer using two significant figures.3.) A mini-black hole with the mass of the Moon. Express your answer using two significant figures.4.) Estimate the Schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that your weight is 50 kg.) Express your answer using one significant figure.

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Thu Thủy 5 years 2021-08-11T04:46:16+00:00 1 Answers 177 views 0

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  1. RuslanHeatt
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    2021-08-11T04:48:02+00:00
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    Answer:

    (I). The Schwarzschild radius is 2.94\times10^{8}\ km

    (II). The Schwarzschild radius is 17.7 km.

    (III). The Schwarzschild radius is 1.1\times10^{-7}\ km

    (IV). The Schwarzschild radius is 7.4\times10^{-29}\ km

    Explanation:

    Given that,

    Mass of black hole m= 1\times10^{8} M_{sun}

    (I). We need to calculate the Schwarzschild radius

    Using formula of radius

    R_{g}=\dfrac{2MG}{c^2}

    Where, G = gravitational constant

    M = mass

    c = speed of light

    Put the value into the formula

    R_{g}=\dfrac{2\times6.67\times10^{-11}\times1\times10^{8}\times1.989\times10^{30}}{(3\times10^{8})^2}

    R_{g}=2.94\times10^{8}\ km

    (II). Mass of block hole m= 6 M_{sun}

    We need to calculate the Schwarzschild radius

    Using formula of radius

    R_{g}=\dfrac{2MG}{c^2}

    Put the value into the formula

    R_{g}=\dfrac{2\times6.67\times10^{-11}\times6\times1.989\times10^{30}}{(3\times10^{8})^2}

    R_{g}=17.7\ km

    (III). Mass of block hole m= mass of moon

    We need to calculate the Schwarzschild radius

    Using formula of radius

    R_{g}=\dfrac{2MG}{c^2}

    Put the value into the formula

    R_{g}=\dfrac{2\times6.67\times10^{-11}\times7.35\times10^{22}}{(3\times10^{8})^2}

    R_{g}=1.1\times10^{-7}\ km

    (IV). Mass = 50 kg

    We need to calculate the Schwarzschild radius

    Using formula of radius

    R_{g}=\dfrac{2MG}{c^2}

    Put the value into the formula

    R_{g}=\dfrac{2\times6.67\times10^{-11}\times50}{(3\times10^{8})^2}

    R_{g}=7.4\times10^{-29}\ km

    Hence, (I). The Schwarzschild radius is 2.94\times10^{8}\ km

    (II). The Schwarzschild radius is 17.7 km.

    (III). The Schwarzschild radius is 1.1\times10^{-7}\ km

    (IV). The Schwarzschild radius is 7.4\times10^{-29}\ km

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