A Body Travels Along a Circular Path of Radius 70m?

Question: A Body Travels along a circular path of radius 70m, What would the average velocity of the body be?

1. 3.5 m/s
2. 7 m/s
3. 14 m/s
4. 35 m/s

Answer: C) 14 m/s

A Body Travels along a circular path of radius 70m Solution:

To calculate the average velocity of the body, we first need to understand that the motion is circular. Since the body completes half a revolution, it travels a distance equal to half the circumference of the circle.

• The formula for the circumference of a circle is given by: Circumference = 2 * π * radius.
• Given that the radius of the circular path is 70 m, the circumference can be calculated as follows: Circumference = 2 * π * 70 = 140 * π ≈ 439.82 m
• As the body travels half a revolution, the distance covered is half of the circumference: Distance covered = 1/2 * 439.82 ≈ 219.91 m
• Now, we can use the formula for average velocity: Average velocity = Total distance covered / Total time taken.
• The distance covered is approximately 219.91 m, and the total time taken is 20 seconds. Let’s calculate the average velocity: Average velocity = 219.91 m / 20 s ≈ 10.9955 m/s

Rounded to two decimal places, the average velocity of the body is approximately 11 m/s.

Therefore, none of the provided options is correct. However, if we round off the average velocity to the nearest whole number, it becomes 11 m/s.

The Arithmetic mean of Three Observations is x

The arithmetic mean of three observations is $x$ when the sum of those observations divided by three equals $x$. Mathematically, if the three observations are represented as $a,b,$ and $c$, then the formula can be expressed as:

x=(a+b+c)/​3

To find the sum of the observations, simply multiply the mean $x$ by 3:

a+b+c=3x

Understanding the arithmetic mean helps in various fields, such as statistics and data analysis, providing a straightforward way to summarize and interpret sets of data effectively.