A rocket is launched with velocity 10 km/s if radius of earth is R, then maximum height attained by it will be

Question

\[(a)\;2\; R \quad (b)\;4\;R \quad (c)\; 3\;R \quad (d)\;5\;R\]

Answer 1

$KE$ given =$P.E$ of the body

$\large\frac{1}{2} $$mv^2=mg (R+h)$

$v^2=2g(R+h)$

Where $'h'$ maximum height reached by the satellite

$\bigg( 10 \times \large\frac{5}{8}\bigg)^2 $$\times 10^6= 2\times 10(R+h)$

Solving we get

$R+h=5R$

Where $R= 6.4 \times 10^6 \;m$

$R+h=5R$

$\quad h=4R$

Hence b is the correct answer.