Give the MKS units for each of the following quantities. (A) Young's modulus (B) Magnetic Induction (C) Power of a lens

Step 1: Determine the MKS unit of Young's modulus.

Young's modulus $Y$ is defined as the ratio of tensile stress to tensile strain.

$$Y = \frac{\text{stress}}{\text{strain}}$$ $$\text{stress} = \frac{F}{A}$$ $$\text{strain} = \frac{\Delta L}{L}$$

Since strain is a dimensionless ratio, the unit of Young's modulus is equal to the unit of stress.

$$[Y] = \frac{[F]}{[A]} = \frac{\text{N}}{\text{m}^2} = \text{Pa}$$

Step 2: Determine the MKS unit of Magnetic Induction.

The magnetic induction $B$ is related to the magnetic force $F$ acting on a charge $q$ moving with velocity $v$.

$$F = qvB$$ $$B = \frac{F}{qv}$$

Substitute the MKS units for force, charge, and velocity.

$$[B] = \frac{[F]}{[q][v]} = \frac{\text{N}}{\text{C} \cdot \text{m/s}}$$ $$[B] = \frac{\text{N}}{\text{A} \cdot \text{m}} = \text{T}$$

Step 3: Determine the MKS unit of the Power of a lens.

The power $P$ of a lens is defined as the reciprocal of its focal length $f$ in meters.

$$P = \frac{1}{f}$$ $$[P] = \text{m}^{-1} = \text{D}$$

Answer:

• (A) Young's modulus: $\text{N/m}^2$ (or $\text{Pa}$)
• (B) Magnetic Induction: $\text{T}$ (or $\text{Wb/m}^2$)
• (C) Power of a lens: $\text{m}^{-1}$ (or $\text{D}$)