If an automobile moves round a curve of radius 300 m at constant speed of `60 m//s`, then the change of velocity round a curve of `60^(@)` will be

Options

A. zero
B. `30m//s`
C. `120 m//s`
D. `60m//s`

Explanation

To solve the problem of finding the change in velocity of an automobile moving around a curve of radius 300 m at a constant speed of 60 m/s while covering a curve of 60 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Radius of the curve (r) = 300 m
- Speed of the automobile (v) = 60 m/s
- Angle of the curve (θ) = 60 degrees

2. **Understand the Concept of Change in Velocity:**
- When an object moves in a circular path, its velocity changes due to the change in direction, even if the speed remains constant. The change in velocity (Δv) can be calculated using the formula:
\[ \Delta v = 2v \sin\left(\frac{\theta}{2}\right) \]

3. **Substitute the Values into the Formula:**
- First, calculate \(\frac{\theta}{2}\):
\[ \frac{\theta}{2} = \frac{60}{2} = 30 \text{ degrees} \]
- Now, substitute v and \(\sin(30^\circ)\) into the formula:
\[ \Delta v = 2 \times 60 \times \sin(30^\circ) \]

4. **Calculate \(\sin(30^\circ)\):**
- We know that \(\sin(30^\circ) = \frac{1}{2}\).

5. **Perform the Calculation:**
- Substitute \(\sin(30^\circ)\) into the equation:
\[ \Delta v = 2 \times 60 \times \frac{1}{2} \]
- Simplify:
\[ \Delta v = 2 \times 60 \times 0.5 = 60 \text{ m/s} \]

6. **Conclusion:**
- The change in velocity when the automobile covers a curve of 60 degrees is:
\[ \Delta v = 60 \text{ m/s} \]

### Final Answer:
The change of velocity around a curve of 60 degrees is **60 m/s**.

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