A train is moving with a speed of 180 km/hr. It's speed in metre per second is :

Question

Accepted Answer

To convert the speed of the train from kilometers per hour (km/hr) to meters per second (m/sec), we use the conversion factor that 1 km/hr is equal to $ \frac{5}{18} $ m/sec. This conversion factor is derived from the fact that 1 kilometer is 1000 meters and 1 hour is 3600 seconds.

Let's apply this conversion to the given speed of the train:

1. **Convert 180 km/hr to m/sec:**

$$
   180 \, \text{km/hr} \times \frac{5}{18} \, \text{m/sec per km/hr} = 50 \, \text{m/sec}
   $$

Therefore, the speed of the train in meters per second is 50 m/sec, which corresponds to Option 1.

2. **Explanation for why Option 1 is correct:**

- The calculation above shows that when you convert 180 km/hr to m/sec using the standard conversion factor, you get 50 m/sec. This matches exactly with Option 1, confirming it as the correct answer.

3. **Explanation for why the other options are incorrect:**

- **Option 2 (40 m/sec):** If you calculate using the conversion factor, 180 km/hr does not equate to 40 m/sec. The correct conversion yields 50 m/sec, not 40 m/sec.
   
   - **Option 3 (30 m/sec):** Similarly, 30 m/sec is not the result of converting 180 km/hr using the correct conversion factor. The calculation clearly shows that the speed is 50 m/sec.
   
   - **Option 4 (25 m/sec):** This option is also incorrect because the conversion of 180 km/hr results in 50 m/sec, not 25 m/sec.

In conclusion, the correct conversion of 180 km/hr to meters per second is 50 m/sec, which is why Option 1 is the correct answer.