Calculate the surface gravitational acceleration of a 1.4-solar-mass neutron sta

Question

Calculate the surface gravitational acceleration of a 1.4-solar-mass neutron star with a radius of 10 kIm Express your answer using two significant figures. x x .IO" In SubmitP nswers Request Ans Incorrect Try Again; 5 attempts remaining Part B Calculate the escape speed of a 1.4-solar-mass neutron star with a radius of 10 km. Express your answer using two significant figures. u= In Submit est Answer Part C What would be the escape speed from a neutron star of the same mass and radius 4 km? Express your answer using two significant figures. In Submit est Answer

Explanation / Answer

(A)

1.4 solar masses = 2.784488 × 10^30 kg

a = Gm/r^2

a = 6.67428 x 10^-11 x 2.784488 × 10^30/10,000^2

a = 1,858,445,256,864 m/s²

= 1.9 x 1012 m/s2

(B)

Ve = sqrt(2GM/r)

Let's take G = 6.67×10^11 m^3 kg^1 s^2 which means we need to know the mass in kg and the radius in metres which will give us escape velocity in metres per second.

1.4 Solar mass = 2.784488 × 10^30 kg

10km = 10,000 m

Ve = sqrt(2(6.67×10^11 m^3 kg^1 s^2 )( 2.784488 × 10^30 kg)/(10,000 m))

= 1.927×10^8 m/s

= 1.9 x 108 m/s

(C)

Now, R = 4km = 4000m

So

Ve = sqrt(2(6.67×10^11 m^3 kg^1 s^2 )( 2.784488 × 10^30 kg)/(4,000 m))

= 3.0 x 108 m/s

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