Question

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter. Part A If you weigh 665 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 16.0 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. View Available Hint(s)

Answer 1

1.41*10^14 N

Step-by-step explanation:

Given that

Weight of the person on earth, W = 665

Radius of the neutron star, r = 8 km

Mass of the sun, M = 1.99*10^30 kg

Gravitational constant, G = 6.67*10^-11 Nm²/kg²

Acceleration due to gravity in earth, g = 9.8 m/s²

Weight on earth is given by

W = mg, so that, mass m would be

m = W/g

m = 665 / 9.8

m = 67.86 kg

The mass on earth is 67.86 kg

Weight on the neutron star is then

W = F = GmM/r²

F = (6.67*10^-11 * 67.86 * 1.99*10^30) / 8000²

F = 9*10^21 / 6.4*10^7

F = 1.41*10^14 N

Thus, the the weight in the neutron star is 1.41*10^14 N