Final answer:
The percentage error in the time period of a pendulum with 2% error in length and 4% error in gravity is calculated to be 3%, combining the individual contributions from length and gravity.
Step-by-step explanation:
The percentage error in the measurement of the time period of a pendulum with maximum errors in measurement of length (l) and acceleration due to gravity (g) can be calculated using the formula for the period of a pendulum T = 2π√(l/g), which is derived from the simple harmonic motion equations for a pendulum. Since the period is directly proportional to the square root of length and inversely proportional to the square root of acceleration due to gravity, the percentage error in the time period can be found by adding the percentage errors of l and g taking into account the square root relationship to T.
Given that the maximum percentage error in measurement of l is 2%, and the error in g is 4%, the total percentage error in the time period T would be:
Percentage error in T due to l = (1/2) × 2% = 1%
Percentage error in T due to g = (1/2) × 4% = 2%
Total percentage error in T = 1% + 2% = 3%.
Therefore, the answer to the student's question is (c) 3%.