GATE 2021 AE – Question 35
The velocity required to launch a space shuttle from the surface of Earth to achieve a circular orbit of altitude 250 km is ___ (two decimals). For Earth, $Gm_e=398600.4$ km³/s² and surface radius $R_0=6378.14$ km.
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Correct answer: 7.75 to 7.77 OR 7750.00 to 7770.00
Explanation
The published key accepts circular-orbit speed: $v=\sqrt{\mu/(R_0+h)}=\sqrt{398600.4/6628.14}=7.755$ km/s. Both 7.75–7.77 km/s and 7750–7770 m/s are explicitly accepted because the stem omits the answer unit. The energy-equivalent launch speed from the surface, about 8.05 km/s, is a different quantity and is not accepted.
Official GATE 2021 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2021/ae_2021.pdf