Answer:
The centripetal acceleration for the first radius; 2.0 m = 50 m/s²
The centripetal acceleration for the second radius; 4.0 m = 25 m/s²
The centripetal acceleration for the third radius; 6.0 m = 16.67 m/s²
The centripetal acceleration for the fourth radius; 8.0 m = 12.5 m/s²
The centripetal acceleration for the fifth radius; 10.0 m = 10 m/s²
Explanation:
Given;
mass of the object, m = 1 kg
velocity of the object, v = 10 m/s
different values of the radius, 2.0 m 4.0 m 6.0 m 8.0 m 10.0 m
The centripetal acceleration for the first radius; 2.0 m
![a_c = \frac{v^2}{r} \\\\a_c_1= \frac{(10)^2}{2} \\\\a_c_1= 50 \ m/s^2](https://tex.z-dn.net/?f=a_c%20%3D%20%5Cfrac%7Bv%5E2%7D%7Br%7D%20%5C%5C%5C%5Ca_c_1%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B2%7D%20%5C%5C%5C%5Ca_c_1%3D%2050%20%5C%20m%2Fs%5E2)
The centripetal acceleration for the second radius; 4.0 m
![a_c_2= \frac{(10)^2}{4} \\\\a_c_2= 25 \ m/s^2](https://tex.z-dn.net/?f=a_c_2%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B4%7D%20%5C%5C%5C%5Ca_c_2%3D%2025%20%5C%20m%2Fs%5E2)
The centripetal acceleration for the third radius; 6.0 m
![a_c_3= \frac{(10)^2}{6} \\\\a_c_3= 16.67 \ m/s^2](https://tex.z-dn.net/?f=a_c_3%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B6%7D%20%5C%5C%5C%5Ca_c_3%3D%2016.67%20%5C%20m%2Fs%5E2)
The centripetal acceleration for the fourth radius; 8.0 m
![a_c_4= \frac{(10)^2}{8} \\\\a_c_4= 12.5 \ m/s^2](https://tex.z-dn.net/?f=a_c_4%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B8%7D%20%5C%5C%5C%5Ca_c_4%3D%2012.5%20%5C%20m%2Fs%5E2)
The centripetal acceleration for the fifth radius; 10.0 m
![a_c_5= \frac{(10)^2}{10} \\\\a_c_5= 10 \ m/s^2](https://tex.z-dn.net/?f=a_c_5%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B10%7D%20%5C%5C%5C%5Ca_c_5%3D%2010%20%5C%20m%2Fs%5E2)