Explanation:
It s given that,
Mass of a planet, 
Radius of a planet, 
(1) We need to find the acceleration due to gravity for a person on the surface of the planet. Its formula is given by :



(2) The escape velocity is given by :


v = 7324.61 m/s
Hence, this is the required solution.
To solve this problem we will begin by finding the necessary and effective distances that act as components of the centripetal and gravity Forces. Later using the same relationships we will find the speed of the body. The second part of the problem will use the equations previously found to find the tension.
PART A) We will begin by finding the two net distances.

And the distance 'd' is



Through the free-body diagram the tension components are given by


Here we can watch that,

Dividing both expression we have that,

Replacing the values,


PART B) Using the vertical component we can find the tension,




Answer:
The magnitude of the torque the bucket produces around the center of the cylinder is 26.46 N-m.
Explanation:
Given that,
Mass of bucket = 54 kg
Radius = 0.050 m
We need to calculate the magnitude of the torque the bucket produces around the center of the cylinder
Using formula of torque


Where, m = mass
g = acceleration due to gravity
r = radius
Put the value into the formula


Hence, The magnitude of the torque the bucket produces around the center of the cylinder is 26.46 N-m.
<u>Answer;</u>
<em>Spring constant </em>
<u>Explanation;</u>
The measure of a spring’s resistance to being compressed or stretched is the <u>spring constant</u>.
- The symbol of spring constant is K, since it is a constant. From the Hooke's law,for a helical spring or any elastic material, the extension force is directly proportional to the extension provided the elastic limit is not exceeded.
- Therefore; the spring constant = Force/extension. That is; K = F/e; where k is the spring constant, F is the extension force and e is the extension.
- Spring constant depicts the resistance of the spring to compressional and stretching forces.
R 1,2 = 27.5 + 33.0 = 60.5 Ohms
1/ R 1,2,3 = 1/ 60.5 + 1 / 22 = 82.5 / 1331
R 1, 2, 3 = 1331 / 82.5 = 16.13 Ohms
I = U / R
I = 9 V / 16.13 Ohms = 0.557 A ≈ 0.56 A
Answer: C ) 0.56 Amps