To find the centripetal force acting on the discus, we can use the following formula for centripetal force (F):
[tex]\[ F = \frac{m v^2}{r} \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( v \)[/tex] is the velocity,
- [tex]\( r \)[/tex] is the radius.
Let's apply the values provided in the problem:
- Mass ([tex]\( m \)[/tex]) = 2.0 kilograms,
- Velocity ([tex]\( v \)[/tex]) = 5.0 meters per second,
- Radius ([tex]\( r \)[/tex]) = 0.75 meters.
Now, we substitute these values into the formula:
[tex]\[ F = \frac{2.0 \, \text{kg} \times (5.0 \, \text{m/s})^2}{0.75 \, \text{m}} \][/tex]
First, calculate the velocity squared:
[tex]\[ (5.0 \, \text{m/s})^2 = 25 \, \text{m}^2/\text{s}^2 \][/tex]
Next, compute the mass times the velocity squared:
[tex]\[ 2.0 \, \text{kg} \times 25 \, \text{m}^2/\text{s}^2 = 50 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
Finally, divide by the radius:
[tex]\[ F = \frac{50 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{0.75 \, \text{m}} \][/tex]
[tex]\[ F = 66.66666666666667 \, \text{N} \][/tex]
The numerical result rounded to the nearest whole number is 67 N, which is closest to the option 66 N given in the problem.
Therefore, the centripetal force acting on the discus is:
[tex]\[ \boxed{66 \, \text{N}} \][/tex]
