Question

The escape velocity corresponding to a planet of mass M and radius R is 50 km/sec. If the planet's mass and radius were 4M and R respectively, then the corresponding escape velocity would be –

• A. 100 km/sec
• B. 50 km/sec
• C. 200 km/sec
• D. 25 km/sec

Answer 1

The correct option is A 100 km/sec

In $1^{st}$ case -
$v_e=\sqrt{\frac{2GM}{R}}$
$50=\sqrt{\frac{2GM}{R}}$
In $2^{nd}$ case -
$V_{e^{\prime }}=\sqrt{\frac{2G\left(4M\right)}{R}}=2\sqrt{\frac{2GM}{R}}$
$=2\times 50=100$ km/sec