Give the MKS units for each of the following question .
(a) Young's modulus (b) Magnetic induction (c) power of a lena

Explanation

To find the MKS units for each of the given quantities, we will analyze each one step by step.

### Step 1: Young's Modulus
Young's modulus (Y) is defined as the ratio of stress to strain.

1. **Stress** is defined as force per unit area. In MKS units, force is measured in Newtons (N) and area in square meters (m²).
\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{\text{N}}{\text{m}^2} \]

2. **Strain** is a dimensionless quantity (it is the ratio of change in length to original length), so it has no units.

3. Therefore, Young's modulus can be expressed as:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\text{N/m}^2}{1} = \text{N/m}^2 \]

4. In MKS units, 1 N/m² is also known as 1 Pascal (Pa). Thus, the MKS unit for Young's modulus is:
\[ \text{MKS unit of Young's modulus} = \text{Pa} \text{ (Pascal)} \]

### Step 2: Magnetic Induction
Magnetic induction (B), also known as magnetic flux density, can be derived from the Lorentz force equation.

1. The force (F) on a charge (q) moving with a velocity (v) in a magnetic field (B) is given by:
\[ F = qvB \]

2. Rearranging this gives:
\[ B = \frac{F}{qv} \]

3. In MKS units:
- Force (F) is in Newtons (N)
- Charge (q) is in Coulombs (C)
- Velocity (v) is in meters per second (m/s)

4. Therefore, the unit of magnetic induction (B) can be expressed as:
\[ B = \frac{\text{N}}{\text{C} \cdot \text{m/s}} = \frac{\text{N} \cdot \text{s}}{\text{C} \cdot \text{m}} \]

5. The unit of magnetic induction is also known as Tesla (T). Thus, the MKS unit for magnetic induction is:
\[ \text{MKS unit of magnetic induction} = \text{T} \text{ (Tesla)} \]

### Step 3: Power of a Lens
The power (P) of a lens is defined as the reciprocal of its focal length (f).

1. The formula for the power of a lens is:
\[ P = \frac{1}{f} \]

2. The focal length (f) is measured in meters (m). Therefore, the unit of power of a lens can be expressed as:
\[ P = \frac{1}{\text{m}} \]

3. The unit of power of a lens is also known as diopter (D). Thus, the MKS unit for the power of a lens is:
\[ \text{MKS unit of power of a lens} = \text{D} \text{ (Diopter)} \]

### Summary of MKS Units
- Young's Modulus: **Pascal (Pa)**
- Magnetic Induction: **Tesla (T)**
- Power of a Lens: **Diopter (D)**