To solve the question "1 dyne = ………… newton", we need to convert the unit of force from dyne (cgs unit) to newton (SI unit). Here’s a step-by-step solution:
### Step 1: Understand the Units
- Dyne is the cgs (centimeter-gram-second) unit of force.
- Newton is the SI (meter-kilogram-second) unit of force.
### Step 2: Define the Relationship
1 newton (N) is defined as the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared. Mathematically, this can be expressed as:
\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \]
### Step 3: Define Dyne
1 dyne is defined as the force required to accelerate a mass of 1 gram at a rate of 1 centimeter per second squared. Mathematically, this can be expressed as:
\[ 1 \, \text{dyne} = 1 \, \text{g} \cdot \text{cm/s}^2 \]
### Step 4: Convert Units
Now, we need to convert grams to kilograms and centimeters to meters:
- \( 1 \, \text{g} = 10^{-3} \, \text{kg} \)
- \( 1 \, \text{cm} = 10^{-2} \, \text{m} \)
### Step 5: Substitute the Values
Substituting the conversions into the dyne equation:
\[ 1 \, \text{dyne} = (10^{-3} \, \text{kg}) \cdot (10^{-2} \, \text{m/s}^2) \]
\[ 1 \, \text{dyne} = 10^{-3} \, \text{kg} \cdot 10^{-2} \, \text{m/s}^2 \]
\[ 1 \, \text{dyne} = 10^{-5} \, \text{kg} \cdot \text{m/s}^2 \]
### Step 6: Relate Dyne to Newton
Since \( 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \), we can express dyne in terms of newton:
\[ 1 \, \text{dyne} = 10^{-5} \, \text{N} \]
### Final Answer
Thus, we conclude that:
\[ 1 \, \text{dyne} = 10^{-5} \, \text{newton} \]
