To find the pressure exerted by the stylus of a phonograph record on the groove, we can use the formula for pressure, which is defined as the force applied per unit area. The formula is: \[ P = \frac{F}{A} \] where: - \( P \) is the pressure, - \( F \) is the force applied, - \( A \) is the area over which the force is applied. ### Step 1: Identify the Given Values From the problem, we have: - Force \( F = 7.7 \times 10^{-2} \, \text{N} \) - Radius of the groove \( r = 10^{-5} \, \text{m} \) ### Step 2: Calculate the Area The area \( A \) over which the force is applied can be calculated using the formula for the area of a circle: \[ A = \pi r^2 \] Substituting the radius into the formula: \[ A = \pi (10^{-5})^2 \] \[ A = \pi (10^{-10}) \, \text{m}^2 \] \[ A \approx 3.14 \times 10^{-10} \, \text{m}^2 \] ### Step 3: Calculate the Pressure Now we can substitute the values of force and area into the pressure formula: \[ P = \frac{F}{A} = \frac{7.7 \times 10^{-2}}{3.14 \times 10^{-10}} \] Calculating this gives: \[ P \approx \frac{7.7 \times 10^{-2}}{3.14 \times 10^{-10}} \approx 2.45 \times 10^{8} \, \text{N/m}^2 \] ### Conclusion Thus, the pressure exerted by the stylus on the groove is approximately: \[ P \approx 2.45 \times 10^{8} \, \text{N/m}^2 \] ### Correct Option The correct option is **A. 2.45 x 10⁸ Nm^-2**. ### Explanation of Other Options - **B. 3.45 x 10⁸ Nm^-2**: This value is higher than the calculated pressure, likely due to an incorrect calculation of either the force or the area. - **C. 4.90 x 10⁸ Nm^-2**: This value is also too high and does not correspond to the calculations based on the given force and area. - **D. 2.42 x 10⁸ Nm^-2**: This value is close but slightly lower than the calculated pressure, indicating a possible rounding error or miscalculation. ### Common Pitfalls - **Forgetting to square the radius**: When calculating the area, it’s crucial to remember to square the radius. - **Using incorrect units**: Ensure that all units are consistent (e.g., using meters for radius and Newtons for force). - **Rounding errors**: Be careful with rounding during calculations, as this can lead to incorrect final answers. ### Revision Summary - Pressure is calculated using \( P = \frac{F}{A} \). - The area of a circle is given by \( A = \pi r^2 \). - Substitute the values carefully to avoid calculation errors. - Always check the units to ensure consistency in calculations.