A wheel of a motor bike has radius 35 cm . How many revolutions per minute must the wheel make so that the speed of the bike is 33 km/hr ?

Options

A. 300
B. 250
C. 200
D. 220

Explanation

To solve the problem, we need to find out how many revolutions per minute a motorbike's wheel must make to achieve a speed of 33 km/hr, given that the radius of the wheel is 35 cm.

### Step-by-Step Solution:

1. **Convert the speed from km/hr to cm/min**:
- Speed in km/hr = 33 km/hr
- To convert km/hr to cm/min, we use the conversion factors:
- 1 km = 100,000 cm
- 1 hour = 60 minutes
- Therefore,
\[ \text{Speed in cm/min} = 33 \times 100,000 \, \text{cm} / 60 \, \text{min} = 55000 \, \text{cm/min} \]

2. **Calculate the circumference of the wheel**:
- The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
- Given the radius \( r = 35 \) cm, we calculate:
\[ C = 2 \times \pi \times 35 \approx 2 \times 3.14 \times 35 \approx 220 \, \text{cm} \]

3. **Determine the number of revolutions per minute**:
- The number of revolutions per minute (RPM) can be calculated by dividing the distance traveled in one minute by the circumference of the wheel:
\[ \text{Revolutions per minute} = \frac{\text{Distance in cm/min}}{\text{Circumference in cm}} = \frac{55000 \, \text{cm/min}}{220 \, \text{cm}} \]
- Performing the division:
\[ \text{Revolutions per minute} = 250 \]

### Final Answer:
The wheel must make **250 revolutions per minute** for the bike to travel at a speed of 33 km/hr.