The value of acceleration due to gravity is ` 980 cm s^(-2)`. What will be its value if the unit of length is kilometer and that of time is minute?

Explanation

To find the value of acceleration due to gravity in different units (kilometers and minutes), we can follow these steps:

### Step 1: Understand the given value
The acceleration due to gravity is given as:
\[ g = 980 \, \text{cm/s}^2 \]

### Step 2: Convert centimeters to kilometers
We know that:
- 1 kilometer = 1000 meters
- 1 meter = 100 centimeters

Thus,
\[ 1 \, \text{km} = 1000 \times 100 \, \text{cm} = 100000 \, \text{cm} = 10^5 \, \text{cm} \]

To convert from centimeters to kilometers:
\[ 1 \, \text{cm} = \frac{1}{10^5} \, \text{km} \]

### Step 3: Convert seconds to minutes
We know that:
- 1 minute = 60 seconds

Thus,
\[ 1 \, \text{s} = \frac{1}{60} \, \text{min} \]

To convert from seconds squared to minutes squared:
\[ 1 \, \text{s}^2 = \left(\frac{1}{60}\right)^2 \, \text{min}^2 = \frac{1}{3600} \, \text{min}^2 \]

### Step 4: Substitute the conversions into the formula
Now we can substitute these conversions into the expression for \( g \):
\[ g = 980 \, \text{cm/s}^2 \]
Converting \( g \) to kilometers and minutes:
\[ g = 980 \times \frac{1}{10^5} \, \text{km} \times \frac{1}{\frac{1}{3600}} \, \text{min}^{-2} \]

### Step 5: Simplify the expression
Now, simplifying this:
\[ g = 980 \times 3600 \times 10^{-5} \, \text{km/min}^2 \]

Calculating the numerical value:
\[ g = 980 \times 36 \times 10^{-2} \, \text{km/min}^2 \]
\[ g = 35280 \times 10^{-2} \, \text{km/min}^2 \]
\[ g = 353 \, \text{km/min}^2 \]

### Final Answer
Thus, the value of acceleration due to gravity in kilometers per minute squared is:
\[ g \approx 3.53 \, \text{km/min}^2 \]

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