A sprinter covers a distance of `2pir` while running across joggers track of circumference 44 cm. Find the work done by the sprinter if the distance travelled by him is `1.76xx10^(3)km`

Options

A. zero J
B. 10J
C. 100J
D. 1000J

Explanation

To solve the problem, we need to determine the work done by the sprinter after covering a specified distance on a jogger's track. Here's the step-by-step solution:

### Step 1: Understand the given information
- The circumference of the jogger's track is given as 44 cm.
- The distance traveled by the sprinter is given as \(1.76 \times 10^3\) km.

### Step 2: Convert the distance traveled into centimeters
To find the work done, we first need to convert the distance from kilometers to centimeters:
1 km = 1000 m
1 m = 100 cm
Thus,
\[ 1 \text{ km} = 1000 \times 100 = 100000 \text{ cm} \]
Now, converting \(1.76 \times 10^3\) km to centimeters:
\[ 1.76 \times 10^3 \text{ km} = 1.76 \times 10^3 \times 100000 \text{ cm} = 1.76 \times 10^8 \text{ cm} \]

### Step 3: Calculate the number of complete laps around the track
Next, we need to find out how many complete laps the sprinter has run. This can be calculated by dividing the total distance traveled by the circumference of the track:
\[ \text{Number of laps} = \frac{\text{Total distance}}{\text{Circumference}} = \frac{1.76 \times 10^8 \text{ cm}}{44 \text{ cm}} \]
Calculating this gives:
\[ \text{Number of laps} = \frac{1.76 \times 10^8}{44} = 4 \times 10^6 \text{ laps} \]

### Step 4: Determine the net displacement
Since the sprinter completes a whole number of laps, the net displacement after running these laps is zero. This is because the sprinter returns to the starting point after each complete lap.

### Step 5: Calculate the work done
Work done is defined as:
\[ \text{Work done} = \text{Force} \times \text{Displacement} \times \cos(\theta) \]
In this case, since the net displacement is zero, the work done will also be zero:
\[ \text{Work done} = 0 \text{ joules} \]

### Final Answer
Thus, the work done by the sprinter is \(0 \text{ joules}\).

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