Answer:
7572 m/s
Explanation:
The force between two masses separated by a distance r is given as:
[tex]F=G\frac{m_1m_2}{r^2}[/tex]
Where F is the attractive force between 2 masses, m1 and m2, r is the distance between the centres of the masses and G is the universal gravitation constant, which is [tex]6.674*10^-11 Nm^2/kg^2[/tex]
The mass of the earth ([tex]m_1[/tex]) is far greater than the mass of the sputnik ([tex]m_2[/tex]). Therefore [tex]m_1m_2=m_1[/tex]. The mass of the sputnik is neglected, therefore:
[tex]F=G\frac{m_1}{r^2}=\frac{(6.674*10^{-11})(5.98*10^{24})}{(6.96*10^6)^2} = 8.2389N[/tex]
But F is actually centripetal acceleration, a = v²/r
[tex]8.2389 = v^2 / 6.96*10^6\\v=7572m/s[/tex]
