The centripetal force required for a 1000 kg car travelling at 36 kmph to take a turn by `90^(@)` in travelling along an arc of length 628 m is

Options

A. 250 N
B. 500 N
C. 1000 N
D. 125 N

Answer

To find the centripetal force required for a 1000 kg car traveling at 36 km/h to take a 90-degree turn along an arc of length 628 m, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed given is 36 km/h. We can convert this to meters per second using the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
Calculating this:
\[ \text{Speed} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 2: Calculate the radius of the turn
The radius \( r \) of the turn can be calculated using the formula:
\[ r = \frac{L}{\theta} \]
where \( L \) is the length of the arc and \( \theta \) is the angle in radians. The angle of 90 degrees can be converted to radians:
\[ \theta = 90^\circ = \frac{\pi}{2} \text{ radians} \]
Now substituting the values:
\[ r = \frac{628 \text{ m}}{\frac{\pi}{2}} = \frac{628 \times 2}{\pi} \approx 400 \text{ m} \]

### Step 3: Calculate the centripetal force
The formula for centripetal force \( F_c \) is given by:
\[ F_c = \frac{m v^2}{r} \]
Substituting the values we have:
- Mass \( m = 1000 \text{ kg} \)
- Velocity \( v = 10 \text{ m/s} \)
- Radius \( r \approx 400 \text{ m} \)

Now substituting these values into the formula:
\[ F_c = \frac{1000 \times (10)^2}{400} = \frac{1000 \times 100}{400} = \frac{100000}{400} = 250 \text{ N} \]

### Final Answer
The centripetal force required is \( 250 \text{ N} \).

---