A satellite having mass $2 \times 10^{4}$ kg is launched into circular orbit at distance of $R$ from the earth surface. Then find additional velocity imparted to spaceship into orbit to over-come the gravitational pull (in km/sec) will be : [If g = 10 m/s², R of earth = 6400 km, Given that escape velocity from surface of earth = 11.2 km/sec.]

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$5.6 \times (\sqrt{2} - 1)$

$4.2 \times (\sqrt{2} - 1)$

$7.0 \times (\sqrt{2} - 1)$

5.6

answer is B.

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Detailed Solution

$V_{a r b i t a l} = \sqrt{\frac{G M}{2 R}} = \sqrt{\frac{g R}{2}} V_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{2 g R} = 11.2 k / \sec . Δ V = \sqrt{g R} - \sqrt{\frac{g R}{2}} 5.6 \times (\sqrt{2} - 1)$

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