The maximum velocity (in `ms^(-1)`) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

Options

A. (a)60
B. (b)30
C. (c)15
D. 25

Answer

To solve the problem of finding the maximum velocity with which a car driver must traverse a flat curve of radius 150 m and a coefficient of friction of 0.6 to avoid skidding, we can follow these steps:

### Step 1: Understand the Forces Involved
When a car moves around a curve, it requires a centripetal force to keep it moving in a circular path. This force is provided by the friction between the tires and the road. The maximum frictional force can be calculated using the formula:
\[ F_r = \mu \cdot m \cdot g \]
where:
- \( F_r \) is the frictional force,
- \( \mu \) is the coefficient of friction (0.6 in this case),
- \( m \) is the mass of the car,
- \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)).

### Step 2: Set Up the Equation for Centripetal Force
The centripetal force required to keep the car moving in a circle is given by:
\[ F_{cp} = \frac{m \cdot v^2}{r} \]
where:
- \( F_{cp} \) is the centripetal force,
- \( v \) is the velocity of the car,
- \( r \) is the radius of the curve (150 m in this case).

### Step 3: Equate the Forces
To avoid skidding, the maximum frictional force must equal the required centripetal force:
\[ F_r = F_{cp} \]
Substituting the expressions for \( F_r \) and \( F_{cp} \):
\[ \mu \cdot m \cdot g = \frac{m \cdot v^2}{r} \]

### Step 4: Cancel Mass and Rearrange the Equation
Since mass \( m \) appears on both sides of the equation, we can cancel it out:
\[ \mu \cdot g = \frac{v^2}{r} \]
Rearranging gives:
\[ v^2 = \mu \cdot g \cdot r \]

### Step 5: Substitute the Known Values
Now, substitute the known values into the equation:
- \( \mu = 0.6 \)
- \( g = 10 \, \text{m/s}^2 \)
- \( r = 150 \, \text{m} \)

So,
\[ v^2 = 0.6 \cdot 10 \cdot 150 \]
\[ v^2 = 0.6 \cdot 1500 \]
\[ v^2 = 900 \]

### Step 6: Calculate the Maximum Velocity
Taking the square root of both sides to find \( v \):
\[ v = \sqrt{900} \]
\[ v = 30 \, \text{m/s} \]

### Final Answer
The maximum velocity with which a car driver must traverse the curve to avoid skidding is:
\[ \boxed{30 \, \text{m/s}} \]

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