The centripetal force required by a 1000 kg car that takes a turn of radius 50 m at a speed of 36 kmph is

Options

A. 1000N
B. 3500N
C. 1600N
D. 2000N

Answer

To find the centripetal force required by a 1000 kg car taking a turn of radius 50 m at a speed of 36 km/h, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed given is 36 km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ \text{Speed in m/s} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 2: Use the formula for centripetal force
The formula for centripetal force (\( F_c \)) is given by:
\[ F_c = \frac{m v^2}{r} \]
where:
- \( m \) is the mass of the car (1000 kg),
- \( v \) is the speed of the car (10 m/s),
- \( r \) is the radius of the turn (50 m).

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ F_c = \frac{1000 \times (10)^2}{50} \]

### Step 4: Calculate the centripetal force
Calculating the above expression:
\[ F_c = \frac{1000 \times 100}{50} = \frac{100000}{50} = 2000 \text{ N} \]

### Final Answer
The centripetal force required by the car is **2000 Newtons**.

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