Final answer:
The question requires the application of the centripetal force concept to find the tension in the string for a rock moving in a horizontal circle. Using the mass, velocity, and radius, we calculate the tension, equating it to the centripetal force.
Step-by-step explanation:
The subject of this question is Physics, and it is aimed at the High School grade level. To determine the tension in the string, we must use the concept of centripetal force which is provided by the tension of the string in circular motion. The tension in the string is the force that keeps the rock moving in a circle at a constant speed.
The formula for centripetal force (Fc) is:
Fc = m * v2 / r
Where:
- m is the mass of the object (rock)
- v is the tangential velocity of the object
- r is the radius of the circular path
First, we need to calculate the tangential velocity of the rock:
Velocity (v) = circumference / time
As the rock is revolving twice every second, the period (T) for one revolution is 0.5 seconds. The circumference (C) of the circle is 2 * π * r.
v = 2 * π * r / T
Substituting the given values:
v = 2 * π * 0.5 m / 0.5 s
v = 2 * π m/s
Now, we can calculate the tension (T) in the string which is equal to the centripetal force:
T = Fc = m * v2 / r
T = 0.25 kg * (2 * π m/s)2 / 0.5 m
After computing the above formula, the tension in the string can be found, which will be the desired solution.