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Chapter 13: Q.41 - Excercises And Problems (page 354)

A rogue black hole with a mass 12times the mass of the sun drifts into the solar system on a collision course with earth. How far is the black hole from the center of the earth when objects on the earth’s surface begin to lift into the air and “fall” up into the black hole? Give your answer as a multiple of the earth’s radius.

Short Answer

Expert verified

Distance of blackhole from center of earth2000Re

Step by step solution

01

Given information

we have mass of earthMe=5.972×1024kg

Mass of black holeMb=12×Msun=12×1.989×1030kg=23.868×1030kg

02

Explanation

Object start to lift in air when net force on them becomes zero

GMbmx2=GMsunmR2eMbx2=MeR2ex=MbMeRex=23.868×10305.972×1024Rex=1999.16Re

So, distance of blackhole from center of earth will be=x+Re

=1999.16Re+Re=2000.16Re

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