The ratio of SI units to CGS units of retardation is

Options

A. `10^(-2)`
B. `10^(2)`
C. 10
D. `10^(-1)`

Explanation

To find the ratio of SI units to CGS units of retardation, we will follow these steps:

### Step 1: Understand the concept of retardation
Retardation is defined as negative acceleration, which means it is the rate at which an object slows down. It is measured in terms of acceleration.

### Step 2: Identify the SI unit of retardation
The SI unit of acceleration (and thus retardation) is meters per second squared (m/s²).

### Step 3: Identify the CGS unit of retardation
In the CGS (centimeter-gram-second) system, the unit of acceleration is centimeters per second squared (cm/s²).

### Step 4: Convert SI unit to CGS unit
1 meter is equal to 100 centimeters. Therefore, 1 m/s² can be converted to CGS units as follows:
\[ 1 \, \text{m/s}^2 = 100 \, \text{cm/s}^2 \]

### Step 5: Set up the ratio of SI unit to CGS unit
Now we can set up the ratio of SI unit to CGS unit:
\[ \text{Ratio} = \frac{\text{SI unit}}{\text{CGS unit}} = \frac{1 \, \text{m/s}^2}{1 \, \text{cm/s}^2} = \frac{100 \, \text{cm/s}^2}{1 \, \text{cm/s}^2} \]

### Step 6: Simplify the ratio
When we simplify this ratio, we find:
\[ \text{Ratio} = 100 \]

### Step 7: Express the ratio in scientific notation
The ratio can also be expressed in scientific notation as:
\[ 100 = 10^2 \]

### Final Answer
Thus, the ratio of SI units to CGS units of retardation is \(10^2\).

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