The escape velocity for the earth is 11.2 km / sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is:

Question

The escape velocity for the earth is 11.2 km / sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is: (A) 56.0 km/sec (B) 280 km/sec (C) 112 km/sec (D) 56 km/sec

Tardigrade Admin · Accepted Answer

v text escape =√(2 G M/R) propto √(M/R), Hence, (vp/ve)=√(Mp/Rp) × (Re/Me) or (vp/ve)=√100 × (1/4)=5 vp=5 × 11.2=56 km / sec

Q. The escape velocity for the earth is $11.2 km / sec$ . The mass of another planet $100$ times mass of earth and its radius is $4$ times radius of the earth. The escape velocity for the planet is:

56.0 km/sec

280 km/sec

112 km/sec

56 km/sec

$v_{escape} = \frac{2 GM}{R} \propto \frac{M}{R}$ ,
Hence, $\frac{v _{p}}{v _{e}} = \frac{M _{p}}{R _{p}} \times \frac{R _{e}}{M _{e}}$
or $\frac{v _{p}}{v _{e}} = 100 \times \frac{1}{4} = 5$
$v_{p} = 5 \times 11.2 = 56 km / sec$

Q. The escape velocity for the earth is 11.2km/sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is: