Gravitation - Result Question 36
41. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $(.$ mass $.=5.98 \times 10^{24} kg)$ have to be compressed to be a black hole?
(a) $10^{-9} m$
(b) $10^{-6} m$
(c) $10^{-2} m$
(d) $100 m$
[2014]
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Answer:
Correct Answer: 41. (c)
Solution:
- (c) From question,
(b) As we know, escape velocity,
$v_e=\sqrt{\frac{2 GM}{R}}=\sqrt{\frac{2 G}{R} \cdot(\frac{4}{3} \pi R^{3} \rho)}$
$v_e \propto R \sqrt{\rho}$
$\therefore \quad \frac{V_e}{V_p}=\frac{R_e}{R_p} \sqrt{\frac{\rho_e}{\rho_p}}$
$\Rightarrow \frac{V_e}{V_p}=\frac{R_e}{2 R_e} \sqrt{\frac{\rho_e}{2 \rho_e}}$
$\therefore \quad$ Ratio $\frac{V_e}{V_p}=1: 2 \sqrt{2}$
