See below and explain fully. A black hole is an object so heavy that neither mat

Question

See below and explain fully.

A black hole is an object so heavy that neither matter nor even light can escape the influence of its gravitational field. Since no light can escape from it, it appears black. Suppose a mass approximately the size of the Earth's mass 7.45 times 10 24 kg is packed into a small uniform sphere of radius r. Use: The speed of light c = 2.99792 times 10 8 m/s. The universal gravitation constant G = 6.67259 times 10-11 N m2 / kg2. Hint: The escape speed must be the speed of light. Based on Newtonian mechanics, determine the limiting radius r0 when this mass (approximately the size of the Earth's mass) becomes a black hole. Answer in units of m Using Newtonian mechanics, how much would a mass of 1.46 mu g weigh at the surface of this super-dense sphere? Answer in units of N

Explanation / Answer

c = sqrt(2GM/r0

ro = 2 * G M /c^2 = (2*6.67*10^-11*7.45*10^24)/(9*10^16) = 11.042555556e?3 m = 11.043 mm

b) W = m*g = m*G* M/ro^2 = (6.67*10^-11*7.45*10^24*1.46*10^-6)/((11.043*10^-3)^2) = 5.949230806e+12 kg

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