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AIIMS 2005
Exam
AIIMS
Year
2005
Subject
Physics
Chapter
Gravitation

AIIMS 2005 · Physics · Gravitation

The condition for a uniform spherical mass m of radius r to be a...

The condition for a uniform spherical mass mm of radius rr to be a black hole is [G=[G= gravitational constant and g=g= acceleration due to gravity]

Options

  1. A(2Gmr)1/2≤c\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c
  2. B(2gmr)1/2=c\left(\frac{2 g m}{r}\right)^{1 / 2}=c
  3. C(2Gmr)1/2≥c\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c
  4. D(gmr)1/2≥c\left(\frac{g m}{r}\right)^{1 / 2} \geq c

Correct answer

C. (2Gmr)1/2≥c\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c

Step-by-step solution

The criterion for a star to be black hole is GMc2R≥12 or, 2GMR≥\frac{G M}{c^2 R} \geq \frac{1}{2} \text{ or, } \sqrt{\frac{2 G M}{R}} \geqc .
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