What force is required to stretched a steel wire of cross sectional area 1 cm² to double its length (Y=2×10¹¹ Nm⁻²)?

Q20

Step 1: The formula for the angle of minimum deviation $\delta_m$ for a prism is

$$\delta_m = (\mu - 1) A$$

where $\mu$ is the refractive index of the prism material and $A$ is the prism angle.

Step 2: Given $A = 60^\circ$ and $\delta_m = 40^\circ$, substitute the values.

$$40^\circ = (\mu - 1) \times 60^\circ$$

Step 3: Solve for $\mu - 1$.

$$\mu - 1 = \frac{40^\circ}{60^\circ} = \frac{2}{3}$$

Step 4: Find $\mu$.

$$\mu = 1 + \frac{2}{3} = \frac{5}{3}$$

\dfrac{5}{3}

Q22

Step 1: Coulomb's law for the electrostatic force $F$ between two point charges $q$ separated by distance $r$ in vacuum is

$$F = k \frac{q^2}{r^2}$$

where $k = 9 \times 10^9 \, \mathrm{N \cdot m^2 / C^2}$.

Step 2: Given $F = 10 \, \mathrm{N}$, $r = 2 \, \mathrm{m}$, substitute the values.

$$$$