Answer:
Tension in the cable = 200.655 × 10^(18) N
Explanation:
The tension in the cable will be the force on the string which is caused by when it holds against the centripetal acceleration.
Now, the formula for centripetal acceleration is given by;
a = v²/R
Now, let's find the velocity.
The circumference is 2πR
We are given that R = 3.85 x 10^(8) m
So, Circumference = 2 × π × 3.85 x 10^(8) = 24.19 × 10^(8) m
We are told the period of the moon orbit is 27.3 days
Distance travelled per day = Circumference/ period
Distance travelled per day = (24.19 × 10^(8))/27.3 = 88608058.608 m/day
Now, a day has 24 hours = 24 × 60 × 60 = 86400 seconds
Thus,
Distance travelled per seconds =
88608058.608/86400 = 1025.556 m/sec
So, from a_c = v²/r,
a_c = 1025.556²/3.85x10^8
a_c = 0.00273 m/s²
Now, Force = Mass x Acceleration = ma
We are given mass = 7.35 x 10^(22) kg
Plugging in the relevant values, we have;
F = 0.00273 x 7.35 x 10^(22)
F = 200.655 × 10^(18) N
