# At what velocity in (km/s) should a body be projected horizontally at a height of 30 km from the ground so that it becomes the satellite of the earth? neglect air friction. (radius of earth is $6370 \;Km$)

$(a)\;7.6 \quad (b)\;7.9 \quad (c)\;9.8 \quad (d)\;11.2$

Orbital velocity $v_0$ required is given by
$v_0=\sqrt {\large\frac{g_0 R^2}{R+h}}$
$\qquad=\sqrt {\large\frac{9.8 \times (6370 \times 10^3)^2}{(6370+30) \times 10^3}}$$m/s$
$\qquad=7.882 km/s$
$\qquad=7.9 \;km/s$
Hence b is the correct answer.
edited Jun 29, 2014