A space ship of mass $2 \times 10 ^ { 4 } \mathrm {~kg}$ 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 $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and radius of earth $= 6400 \mathrm {~km}$): (1) $11.2 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$ (2) $8 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$ (3) $7.9 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$ (4) $7.4 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$
A space ship of mass $2 \times 10 ^ { 4 } \mathrm {~kg}$ 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 $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and radius of earth $= 6400 \mathrm {~km}$):\\
(1) $11.2 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$\\
(2) $8 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$\\
(3) $7.9 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$\\
(4) $7.4 ( \sqrt { 2 } - 1 ) \mathrm { km } \mathrm { s } ^ { - 1 }$