Question

A research satellite of mass $200kg$ circles the earth in an orbit radius $\frac{3 R_{E}}{2},$ where $R_{E}$ is the radius of the earth. Assuming the gravitational pull on a mass of $1kg$ on the earth's surface to be $10N,$ the pull on the satellite will be :

• A. $890N$
• B. $889N$
• C. $885N$
• D. $892N$

Answer 1

Answer: (B)

$F=\frac{GM_{E} \times 1}{R_{E}^{2}}$ ...(1)
Force between earth and mass $1kg.$
Force between earth and satellite is
$F^{'}=\frac{\left(GM\right)_{E} \times 200}{\left(\frac{3}{2} R_{E}\right)^{2}}$ ...(2)
$\frac{F^{'}}{F}=\frac{8 w}{9}\Rightarrow F^{'}=\frac{8 w}{9}F$
$=\frac{8 W}{9}\times 10N=889N$