Question

A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be

• A. $3 \mathrm {~km} / \mathrm { s }$
• B.
• C. $7.15 \mathrm {~km} / \mathrm { s }$
• D. $8 \mathrm {~km} / \mathrm { s }$

Answer 1

Answer: (C)

$7.15 \mathrm {~km} / \mathrm { s }$

Answer 2

$v _ { 0 } = \sqrt { \frac { G M } { r } } = \sqrt { \frac { g R ^ { 2 } } { r } } = \sqrt { \frac { 10 \times \left( 64 \times 10 ^ { 5 } \right) ^ { 2 } } { 8000 \times 10 ^ { 3 } } }$

$= 71.5 \times 10 ^ { 2 } \mathrm {~m} / \mathrm { s } = 7.15 \mathrm {~km} / \mathrm { s }$