A small mass of 2kg tide to the string of length 3cm complete 4 revolution in one second inhorizontal circle. What is the tangential displacement of the body in 5seconds
To find the tangential displacement of an object moving in a circular path, we can use the formula:
Tangential displacement = 2πrN,
where:
- r is the radius of the circle,
- N is the number of revolutions completed in the given time period.
In this case, we are given the length of the string (3 cm), which is also the radius of the circular path. However, it's important to convert this to meters, as the unit for displacement is meters. So, r = 3 cm = (3/100) m = 0.03 m.
Next, we are told that the small mass completes 4 revolutions in 1 second. To find the number of revolutions in 5 seconds, we need to multiply by the time ratio: 5 seconds / 1 second = 5.
Therefore, N = 4 revolutions * 5 = 20 revolutions.
Now we can substitute these values into the formula:
Tangential displacement = 2πrN = 2 * π * 0.03 * 20 = π * 0.6 ≈ 1.88 m.
Hence, the tangential displacement of the body in 5 seconds is approximately 1.88 meters.