Explanation 1) Concept: We can find the difference between acceleration due to gravity at r = 50 R h and r = 50 R h + r . Using this, we can find the mass of the black hole. Also we can estimate whether our body can tolerate upper lime or lower limit. 2) Given: i) The radius of black hole is R h = 2 G M c 2 ii) The distance of black hole from event horizon is 50 R h . iii) Maximum difference in gravitational acceleration between your feet and head is d a g = 10 m / s 2 3) Formulae: i) F = G M m r 2 ii) F = m a g 4) Calculations: a) Equating the gravitational force of attraction and the gravitational force by Newton’s second law, we get G M m r 2 = m a g This gives a g = G M r 2 Maximum difference in gravitational acceleration between your feet and head is d a g = d G M r 2 d a g = 2 G M r 3 d r d a g = 2 G M 50 R h + h 3 d r = 10 Since h < < 50 R h , we can write h ~ d R and 50 R h + h ~ 50 R h

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ISBN: 9781119500100

Author: Halliday

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 13, Problem 70P

To determine

To find:

a) The limit to the mass of the black hole as a multiple of sun’s mass Ms you can tolerate at the given radial distance (your height).

b) Whether the limit is an upper limit or a lower limit.

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Chapter 13, Problem 69P

Chapter 13, Problem 71P

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Chapter 13 Solutions

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a) The limit to the mass of the black hole as a multiple of sun’s mass Ms you can tolerate at the given radial distance (your height). b) Whether the limit is an upper limit or a lower limit.

Solution Summary: The author explains that the limit to the mass of the black hole as a multiple of sun’s mass Ms is 111 solar masses.

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To find: a) The limit to the mass of the black hole as a multiple of sun’s mass Ms you can tolerate at the given radial distance (your height). b) Whether the limit is an upper limit or a lower limit.

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Chapter 13 Solutions

To find:

a) The limit to the mass of the black hole as a multiple of sun’s mass Ms you can tolerate at the given radial distance (your height).

b) Whether the limit is an upper limit or a lower limit.