The correct order in which the ratio of SI unit to CGS unit increases is
(a) Power (b) Surface tension
(c) Pressure (d) force

Options

A. c,b,d,a
B. c,a,b,d
C. d,a,b,c
D. a,c,d,b

Answer

To solve the problem of determining the correct order in which the ratio of SI units to CGS units increases for the given physical quantities (Power, Surface Tension, Pressure, and Force), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the SI and CGS Units for Each Quantity**:
- **Power**:
- SI Unit: Joule per second (J/s)
- CGS Unit: Erg per second (erg/s)
- **Surface Tension**:
- SI Unit: Newton per meter (N/m)
- CGS Unit: Dyne per centimeter (dyne/cm)
- **Pressure**:
- SI Unit: Pascal (Pa) or Newton per meter squared (N/m²)
- CGS Unit: Dyne per centimeter squared (dyne/cm²)
- **Force**:
- SI Unit: Newton (N)
- CGS Unit: Dyne (dyne)

2. **Convert Each Unit to the Other System**:
- **Power**:
- 1 Joule = \(10^7\) Erg
- Therefore, the ratio of SI to CGS for Power = \( \frac{1 \text{ J/s}}{1 \text{ erg/s}} = 10^7 \)
- **Surface Tension**:
- 1 Newton = \(10^5\) Dyne
- 1 meter = \(10^2\) centimeters
- Therefore, the ratio of SI to CGS for Surface Tension = \( \frac{10^5 \text{ dyne/m}}{10^2 \text{ dyne/cm}} = 10^3 \)
- **Pressure**:
- 1 Newton = \(10^5\) Dyne
- 1 meter² = \(10^4\) centimeters²
- Therefore, the ratio of SI to CGS for Pressure = \( \frac{10^5 \text{ dyne/m}^2}{10^4 \text{ dyne/cm}^2} = 10 \)
- **Force**:
- Therefore, the ratio of SI to CGS for Force = \( \frac{1 \text{ N}}{1 \text{ dyne}} = 10^5 \)

3. **List the Ratios**:
- Power: \(10^7\)
- Surface Tension: \(10^3\)
- Pressure: \(10\)
- Force: \(10^5\)

4. **Order the Ratios**:
- Pressure: \(10\)
- Surface Tension: \(10^3\)
- Force: \(10^5\)
- Power: \(10^7\)

5. **Write the Correct Order**:
- The increasing order of the ratio of SI unit to CGS unit is:
- Pressure < Surface Tension < Force < Power

### Final Answer:
The correct order in which the ratio of SI unit to CGS unit increases is:
(c) Pressure < (b) Surface Tension < (d) Force < (a) Power.