A particle is rotating in a circle of radii r=2/pi m with constant spe...
Explanation:
To find the time interval when the particle completes 1/4th of the circle, we need to determine the time it takes to cover one-fourth of the circumference of the circle.
Step 1: Calculate the circumference of the circle:
The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius is given as r = 2/π m.
C = 2π(2/π) = 4 m
Step 2: Calculate the time taken to cover the whole circumference:
We know that the speed of the particle is constant and equal to 1 m/s. The formula to calculate the time taken to cover a distance is t = d/v, where d is the distance and v is the speed.
In this case, the distance is equal to the circumference of the circle, which is 4 m. Therefore, the time taken to cover the whole circumference is:
t = 4 m / 1 m/s = 4 s
Step 3: Calculate the time taken to cover 1/4th of the circumference:
To find the time taken to cover 1/4th of the circumference, we divide the total time taken to cover the whole circumference by 4.
t = 4 s / 4 = 1 s
Therefore, the time interval when the particle completes 1/4th of the circle is 1 second.
Conclusion:
The average speed (p) of the particle is not required to find the time interval when it completes 1/4th of the circle. The time interval is determined solely by the time taken to cover the distance, which is given by the formula t = d/v. In this case, the time interval is 1 second.