The value of acceleration due to gravity at a place is `9.8ms^(-2)`. Find its value in `km h^(-2)`

Answer

To convert the acceleration due to gravity from meters per second squared (m/s²) to kilometers per hour squared (km/h²), we can follow these steps:

### Step 1: Understand the conversion factors
1. We know that 1 kilometer (km) = 1000 meters (m).
2. We also know that 1 hour (h) = 3600 seconds (s).

### Step 2: Convert meters to kilometers
To convert the acceleration from m/s² to km/s², we divide the value by 1000:
\[ g = 9.8 \, \text{m/s}^2 = \frac{9.8}{1000} \, \text{km/s}^2 = 0.0098 \, \text{km/s}^2 \]

### Step 3: Convert seconds squared to hours squared
Next, we need to convert seconds squared to hours squared. Since 1 hour = 3600 seconds, we have:
\[ 1 \, \text{s}^2 = \left(\frac{1}{3600} \, \text{h}\right)^2 = \frac{1}{3600^2} \, \text{h}^2 \]
Thus, we multiply the km/s² value by \(3600^2\):
\[ g = 0.0098 \, \text{km/s}^2 \times 3600^2 \, \text{h}^2 \]

### Step 4: Calculate \(3600^2\)
Calculating \(3600^2\):
\[ 3600^2 = 12960000 \]

### Step 5: Final calculation
Now, we can calculate the final value:
\[ g = 0.0098 \, \text{km/s}^2 \times 12960000 \, \text{h}^2 = 127.008 \, \text{km/h}^2 \]

### Conclusion
Thus, the value of acceleration due to gravity in km/h² is:
\[ g \approx 127.008 \, \text{km/h}^2 \]