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  • Need clarity, kindly explain! - Gravitation - NEET

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximately radius would earth (mass=5.98X10^{24} kg) have to be compressed to be a black hole?

  • Option 1)

    10^{-9}m

  • Option 2)

    10^{-6} m

  • Option 3)

    10^{-2} m

  • Option 4)

    100m

 

Answers (1)

As we learnt in

Escape velocity ( in terms of radius of planet) -

V_{c}=sqrt{frac{2GM}{R}}

V_{c}=sqrt{2gR}

V_{c} ightarrow Escape velocity

R ightarrowRadius of earth

- wherein

  • depends on the reference body
  • greater the value of frac{M}{R} or left ( gR ight ) greater will be the escape velocity V_{e}=11.2Km/s  For earth

 

 V=\sqrt{\frac{2Gm}{R}}=C

R=\frac{2Gm}{C^{2}}

\frac{2\times 6.67\times 10^{-11}\times 5.98\times 10^{24}}{\left ( 3.8\times 10^{8} \right )^2}=10^{-2}m


Option 1)

10^{-9}m

Incorrect Option

Option 2)

10^{-6} m

Incorrect Option

Option 3)

10^{-2} m

Correct Option

Option 4)

100m

Incorrect Option

Posted by

Vakul

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