If 'muscle times speed equals power', then what is the ratio of the SI unit and the CGS unit of muscle?

Options

A. `10^(5)`
B. `10^(3)`
C. `10^(7)`
D. `10^(-5)`

Explanation

To solve the problem, we need to find the ratio of the SI unit of muscle to the CGS unit of muscle, given that "muscle times speed equals power".

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We start with the equation given in the question:
\[ \text{Muscle} \times \text{Speed} = \text{Power} \]
This implies that:
\[ \text{Muscle} = \frac{\text{Power}}{\text{Speed}} \]

2. **Units of Power and Speed**:
- The SI unit of power is the watt (W), which is equivalent to joules per second (J/s).
- The SI unit of speed is meters per second (m/s).

3. **Expressing Power in SI Units**:
The SI unit of work (energy) is joules (J), where:
\[ 1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]
Therefore, the SI unit of power can be expressed as:
\[ 1 \text{ W} = 1 \text{ J/s} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^3 \]

4. **Substituting Units into the Muscle Equation**:
Now substituting the units of power and speed into the muscle equation:
\[ \text{Muscle (SI)} = \frac{1 \text{ W}}{1 \text{ m/s}} = \frac{1 \text{ kg} \cdot \text{m}^2/\text{s}^3}{1 \text{ m/s}} = 1 \text{ kg} \cdot \text{m/s}^2 \]
Thus, the SI unit of muscle is equivalent to newtons (N), where:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]

5. **Finding the CGS Unit of Muscle**:
In the CGS system, the unit of force is the dyne, where:
\[ 1 \text{ dyne} = 1 \text{ g} \cdot \text{cm/s}^2 \]
To convert from SI to CGS:
\[ 1 \text{ kg} = 10^3 \text{ g} \]
\[ 1 \text{ m} = 10^2 \text{ cm} \]
Therefore, the conversion of newtons to dynes is:
\[ 1 \text{ N} = 10^3 \text{ g} \cdot \frac{10^2 \text{ cm}}{(1 \text{s})^2} = 10^5 \text{ dyne} \]

6. **Calculating the Ratio**:
Now we have:
- SI unit of muscle = 1 N = \(10^5\) dyne
- CGS unit of muscle = 1 dyne
Thus, the ratio of the SI unit to the CGS unit of muscle is:
\[ \text{Ratio} = \frac{10^5 \text{ dyne}}{1 \text{ dyne}} = 10^5 \]

### Final Answer:
The ratio of the SI unit to the CGS unit of muscle is \(10^5\).