Answer:
Radial acceleration of moon is [tex]a_{r} = 2.246\times 10^{-3}[/tex][tex]\frac{m}{s^{2} }[/tex]
Explanation:
Given :
Time period [tex]T = 1.987 \times 10^{6}[/tex] sec
Distance from center of moon to planet [tex]r = 225 \times 10^{6}[/tex] m
From the equation of radial acceleration,
[tex]a_{r} = r\omega ^{2}[/tex]
Where [tex]\omega = 2\pi f = \frac{2\pi }{T}[/tex]
So [tex]\omega = 3.16 \times 10^{-6} \frac{rad}{s}[/tex]
Now moon's radial acceleration,
[tex]a_{r} = 225 \times 10^{6} \times (3.16 \times 10^{-6} )^{2}[/tex]
[tex]a_{r} = 2246.76 \times 10^{-6}[/tex]
[tex]a_{r} = 2.246\times 10^{-3}[/tex] [tex]\frac{m}{s^{2} }[/tex]
