If you weigh 690 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter

Question

If you weigh 690 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 15.0 km ? Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , and the free-fall acceleration at the earth’s surface to be g = 9.8 m/s2 . Express your weight wstar in newtons.

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Xavia 2 months 2021-08-17T02:06:09+00:00 1 Answers 8 views 0

Answers ( )

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    2021-08-17T02:07:34+00:00

    Answer:

    W’ = 1.66 x 10¹⁴ N

    Explanation:

    First, we will calculate the mass:

    W = mg

    where,

    W = weight on earth = 690 N

    m = mass = ?

    g = acceleration due to gravity on earth = 9.8 m/s²

    Therefore,

    m = \frac{W}{g} = \frac{690\ N}{9.8\ m/s^2}\\\\m = 70.4\ kg

    Now, we will calculate the value of g on the neutron star:

    g' = \frac{GM}{R^2}

    where,

    g’ = acceleration due to gravity on the surface of the neutron star = ?

    G = Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

    M = Mass of the Neutron Star = 1.99 x 10³⁰ kg

    R = Radius of the Neutron Star = 15 km/2 = 7.5 km = 7500 m

    Therefore,

    g' = \frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(1.99\ x\ 10^{30}\ kg)}{(7500\ m)^2}\\\\g' = 2.36\ x\ 10^{12}\ m/s^2

    Therefore, the weight on the surface of the neutron star will be:

    W' = mg'\\W' = (70.4\ kg)(2.36\ x\ 10^{12}\ m/s^2)

    W’ = 1.66 x 10¹⁴ N

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