The pair of quantities haivng neither units nor dimensions is

Options

A. plane angle and specific gravity
B. Magnetic permeability and Relative permittive
C. Coefficient of friction of coefficient of restitution
D. Linear moment and Angular momentum

Answer

To solve the question regarding which pair of quantities has neither units nor dimensions, we will analyze each option given in the question step by step.

### Step 1: Analyze Plane Angle
- A plane angle is measured in radians or degrees.
- Radians are derived from the ratio of two lengths (arc length to radius), which means it has a dimension.
- **Conclusion**: Plane angle has units (radians/degrees) and dimensions.

**Hint**: Check if the quantity is measured in a standard unit.

### Step 2: Analyze Magnetic Permeability
- Magnetic permeability (μ) is a measure of how much a material responds to a magnetic field.
- It has units (Henry per meter, H/m) and therefore has dimensions.
- **Conclusion**: Magnetic permeability has units and dimensions.

**Hint**: Consider the physical meaning of the quantity and its relation to other quantities.

### Step 3: Analyze Coefficient of Friction
- The coefficient of friction (μ) is defined as the ratio of the force of friction to the normal force.
- Since it is a ratio of two forces (both measured in Newtons), the units cancel out.
- **Conclusion**: The coefficient of friction is a unitless quantity and has no dimensions.

**Hint**: Look for quantities defined as ratios; they may be unitless.

### Step 4: Analyze Coefficient of Restitution
- The coefficient of restitution is defined similarly to the coefficient of friction; it is the ratio of relative velocities.
- Since it is a ratio, it is also unitless.
- **Conclusion**: The coefficient of restitution is a unitless quantity and has no dimensions.

**Hint**: Identify if the quantity is a ratio of similar dimensions.

### Step 5: Analyze Linear and Angular Momentum
- Linear momentum (p) is defined as mass times velocity (kg·m/s), and angular momentum (L) is defined as the product of moment of inertia and angular velocity (kg·m²/s).
- Both quantities have units and dimensions.
- **Conclusion**: Linear and angular momentum have units and dimensions.

**Final Conclusion**: The pair of quantities that have neither units nor dimensions is the coefficient of friction and the coefficient of restitution.

### Final Answer:
The answer is option C: Coefficient of Friction and Coefficient of Restitution.