Question

Two stars have masses $5\times {10}^{30}$ kg and $7.5\times {10}^{30}$ kg respectively. If they ultimately convert into black holes, the ratio of Schwarzschild radius of the black holes is

• A. $2:3$
• B. $4:9$
• C. $3:2$
• D. $9:4$

Answer 1

The correct option is A $2:3$

Schwarzschild radius is given by:

$R=\frac{2GM}{C^2}$

$\Rightarrow \frac{R_1}{R_2}=\frac{M_1}{M_2}=\frac{5\times {10}^{30}}{7.5\times {10}^{30}}=\frac{50}{75}=\frac{2}{3}$