Final answer:
The pressure exerted by the phonograph needle is calculated using the force applied by the needle's mass (converted to newtons) over the area of the tip's circle (converted to square meters). The result is approximately 7.96×10³ N/m².
Step-by-step explanation:
To calculate the pressure exerted by the phonograph needle, we first need to convert the mass of the needle from grams to kilograms, since the standard unit for force (weight in this context) in the International System of Units (SI) is the newton (N), and 1 N is equivalent to 1 kg·m/s². The mass of the needle is given as 1.00 g, which is equal to 0.001 kg. Using the acceleration due to gravity (g = 9.8 m/s²), the formula for force (F = mg), the weight of the needle is:
F = m × g = 0.001 kg × 9.8 m/s² = 0.0098 N
Next, we determine the area over which this force is exerted, which is the area of the circle formed by the needle's tip. The radius (r) is provided in millimeters, so we must convert it to meters: r = 0.200 mm = 0.0002 m. The area (A) of a circle is calculated using the formula A = πr²:
A = π × (0.0002 m)² = 1.256×10⁻⁷ m²
Finally, pressure (P) is defined as the force applied per unit area, so using the formula P = F/A, the pressure is
P = 0.0098 N / 1.256×10⁻⁷ m² ≈ 7.796×10⁴ N/m²
Therefore, the correct answer is 7.96×10³ N/m², or option 1.