A stone wirelesd at the rope 30cm long makes 10 complete revolution in 25 second
What is this word? wirelesd
To find the linear speed of the stone, we need to calculate the distance traveled per unit time.
1. First, let's find the circumference of the circular path the stone follows:
Circumference = 2 * π * radius
Radius = length of the rope = 30 cm
Circumference = 2 * 3.14 * 30 cm ≈ 188.4 cm
2. Since the stone completes 10 revolutions in 25 seconds, we can find the distance traveled in one revolution by dividing the circumference by the number of revolutions:
Distance traveled in one revolution = Circumference / Number of revolutions
Distance traveled in one revolution = 188.4 cm / 10 ≈ 18.84 cm
3. Finally, we can calculate the linear speed of the stone by dividing the distance traveled in one revolution by the time taken for one revolution:
Linear speed = Distance traveled in one revolution / Time taken for one revolution
Time taken for one revolution = Total time taken / Number of revolutions
Time taken for one revolution = 25 s / 10 = 2.5 s
Linear speed = 18.84 cm / 2.5 s ≈ 7.54 cm/s
Therefore, the linear speed of the stone is approximately 7.54 cm/s.
To find the speed of the stone, we need to determine the distance covered by the stone in one complete revolution and then divide it by the time taken for one complete revolution.
First, let's calculate the length of the path covered by the stone in one complete revolution. Since the stone is attached to a rope that is 30 cm long, the distance covered in one revolution would be equal to the circumference of a circle with a radius of 30 cm.
The formula to calculate the circumference of a circle is: C = 2πr, where C is the circumference and r is the radius.
Given that the radius (r) is 30 cm, we can substitute this value into the formula:
C = 2π(30) = 60π cm
Now, we need to find the time taken for one complete revolution. It is given in the problem that the stone takes 25 seconds to complete 10 revolutions. So we can calculate the time taken for one revolution by dividing 25 seconds by 10:
Time taken for one revolution = 25 seconds / 10 = 2.5 seconds
Finally, to find the speed of the stone, we divide the distance (circumference) covered in one revolution by the time taken for one revolution:
Speed = Distance / Time
Speed = (60π cm) / (2.5 seconds)
To simplify the answer, we can use a calculator to estimate the value of π to 3.14, and then solve the equation:
Speed ≈ (60 × 3.14 cm) / (2.5 seconds)
Speed ≈ 75.36 cm / 2.5 seconds
Speed ≈ 30.14 cm/s (rounded to two decimal places)
Therefore, the speed of the stone is approximately 30.14 cm/s.