A space ship of mass 2 × 10⁴ kg is launched into a circular orbit… | JEE Main 2023 (11 Apr, Shift 2)

Q37JEE Main 2023 · 11 APR · SHIFT 2Medium

Escape Velocity

A space ship of mass $2 \times 10^{4}\text{ kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g = 10\text{ m/s}^{2}$ and radius of earth $= 6400\text{ km}$ ):

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Answer: (d)

Orbit close to the surface: $v_o = \sqrt{gR}$ ; escape speed from there: $v_e = \sqrt{2gR} = \sqrt{2}\,v_o$ .
$v_o = \sqrt{10 \times 6.4 \times 10^{6}} = 8 \times 10^{3}\text{ m/s} = 8\text{ km/s}$
Extra speed $= v_e - v_o = 8(\sqrt{2}-1)\text{ km/s}$ (mass is not needed).
So the answer is (d) $8(\sqrt{2}-1)\text{ km/s}$ .

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Escape Velocity question from JEE Main 2023 (11 Apr, Shift 2)

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