A cosmonaut is orbiting the earth in a spaceraft at an altitude h= 630 km with a speed of 8 km /s .The radius of the earth is 6400 km. What is the approximate value of the acceleration of the cosmonaut ?

Options

A. `10m//s^(2)`
B. `9m//s^(2)`
C. `8 m//s^(2)`
D. `11 m//s^(2)`

Answer

B

Explanation

The acceleration of the cosmonaut is ` a = (v^(2))/(r ) `
where `v= 8 km //s = 800 m//s = 8xx10^(3) m//s`
and r is the distance from the centre of the earth
` therefore r= 6400 km + 800 km = 7200 km = 7.2 xx10^(6) ` m
` therefore a= (v^(2))/(r ) = (8xx10^(3)xx8xx10^(3) )/(7.2xx10^(6))`
`= (64)/(7.2 ) underset(*) overset(*) = 9 m//s^(2)`