The escape velocity for a planet whose radius is \(1.7 \times 10^6 \mathrm{~m}\) and acceleration due to…
The escape velocity for a planet whose radius is \(1.7 \times 10^6 \mathrm{~m}\) and acceleration due to gravity is \(1.7 \mathrm{~ms}^{-2}\) is
\(1.7 \mathrm{kms}^{-1}\)
\(2.89 \mathrm{kms}^{-1}\)
\(1.7 \sqrt{2} \mathrm{kms}^{-1}\)
\(3.4 \mathrm{kms}^{-1}\)
Solution
Radius of planet, \(R=1.7 \times 10^6 \mathrm{~m}\)
Acceleration due to gravity, \(g=1.7 \mathrm{~ms}^{-2}\)
\(\therefore\) Escape velocity on the surface of planet is given as
\(\begin{aligned}
v_e & =\sqrt{2 g R}=\sqrt{2 \times 1.7 \times 1.7 \times 10^6} \\
& =1.7 \sqrt{2} \times 10^3 \mathrm{~ms}^{-1}=1.7 \sqrt{2} \mathrm{~km} \mathrm{~s}^{-1}
\end{aligned}\)