An artificial satellite is moving in a circular orbit around the earth with a speed equal to half of the magnitude of escape velocity from the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth, then speed $(i n m s^{- 1})$ with which it hits the surface of the earth is $\sqrt{k g R} .$ Find the value of k. $(G i v e n g = 9.8 m s^{- 2} a n d R = 6.4 \times 10^{6} m)$

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given, $v_{0} = \frac{v_{e}}{2}$

$\begin{array}{l} \sqrt{\frac{G M}{R + h}} = \frac{1}{2} \sqrt{\frac{2 G M}{R}} \\ h = R \end{array}$

When the satellite stops, $K = 0$

$\begin{array}{l} - \frac{G M m}{2 R} - (- \frac{G M m}{R}) = \frac{1}{2} m v^{2} \\ v = \sqrt{g R} \end{array}$

Watch 3-min video & get full concept clarity