A boy completes one round of a circular track of radius 20 m in 50 seconds. The displacement at the end of 4 minute 10 second will be

Options

A. 40 m
B. 20 m
C. `80 pi m`
D. Zero

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Problem
The boy completes one round of a circular track with a radius of 20 m in 50 seconds. We need to find the displacement after 4 minutes and 10 seconds.

**Hint:** Remember that displacement in circular motion depends on the starting and ending points.

### Step 2: Calculate the Circumference of the Circular Track
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
Where \( r \) is the radius of the circle. Here, \( r = 20 \, \text{m} \).

\[ C = 2 \pi \times 20 = 40 \pi \, \text{m} \]

**Hint:** The circumference is the total distance covered in one complete revolution.

### Step 3: Determine the Total Time in Seconds
Convert 4 minutes and 10 seconds into seconds:
\[ 4 \, \text{minutes} = 4 \times 60 = 240 \, \text{seconds} \]
Adding the additional 10 seconds:
\[ 240 + 10 = 250 \, \text{seconds} \]

**Hint:** Always convert time into the same unit for consistency.

### Step 4: Calculate the Number of Complete Revolutions
To find out how many complete revolutions the boy makes in 250 seconds, we first find out how many seconds it takes for one revolution:
\[ \text{Time for one revolution} = 50 \, \text{seconds} \]
Now, divide the total time by the time for one revolution:
\[ \text{Number of revolutions} = \frac{250 \, \text{seconds}}{50 \, \text{seconds/revolution}} = 5 \]

**Hint:** The number of revolutions tells you how many times he goes around the track.

### Step 5: Determine the Angular Displacement
Since he completes 5 full revolutions, the angular displacement in radians is:
\[ \text{Angular displacement} = 5 \times 2\pi = 10\pi \, \text{radians} \]

**Hint:** Each complete revolution corresponds to an angular displacement of \( 2\pi \) radians.

### Step 6: Calculate the Displacement
Displacement in circular motion is the straight-line distance from the starting point to the ending point. After 5 complete revolutions, the boy returns to his starting point. Therefore, the displacement is:
\[ \text{Displacement} = 0 \, \text{m} \]

**Hint:** Displacement is zero when the starting and ending points coincide.

### Final Answer
The displacement at the end of 4 minutes and 10 seconds is \( 0 \, \text{m} \).