A cyclist rides round a curved path of radius 10m at a speed 18 kmph. If the cycle and the rider together have a mass of 100 kg, the firctional force the ground exerts on the wheel is (g = 10 `ms^(2)`)

Options

A. 250 N
B. 400 N
C. 500 N
D. 600 N

Answer

To solve the problem, we will follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed given is 18 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ V = 18 \text{ km/h} \times \frac{5}{18} = 5 \text{ m/s} \]

### Step 2: Identify the mass of the cyclist and the cycle
The total mass \( m \) of the cyclist and the cycle is given as:
\[ m = 100 \text{ kg} \]

### Step 3: Use the formula for centripetal force
When the cyclist is moving in a circular path, the frictional force acting on the wheels provides the necessary centripetal force to keep the cyclist moving in that path. The formula for centripetal force \( F_c \) is:
\[ F_c = \frac{mv^2}{r} \]
where:
- \( m \) is the mass,
- \( v \) is the speed,
- \( r \) is the radius of the path.

### Step 4: Substitute the values into the centripetal force formula
Given:
- \( m = 100 \text{ kg} \)
- \( v = 5 \text{ m/s} \)
- \( r = 10 \text{ m} \)

Substituting these values into the formula:
\[ F_c = \frac{100 \text{ kg} \times (5 \text{ m/s})^2}{10 \text{ m}} \]

### Step 5: Calculate the centripetal force
Calculating the above expression:
\[ F_c = \frac{100 \times 25}{10} = \frac{2500}{10} = 250 \text{ N} \]

### Step 6: Conclusion
The frictional force that the ground exerts on the wheel is:
\[ F_{\text{friction}} = 250 \text{ N} \]

### Final Answer
The frictional force the ground exerts on the wheel is **250 N**.

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