Question

A student performs an experiment with a simple pendulum and measures the time for 10 vibrations. If he measures the time for 100 vibrations, the relative error in the measurement of the time period will be reduced by?

a) 10%
b) 20%
c) 50%
d) 90%

Answer 1

• d) 90%

Step-by-step explanation:

The relative error in the measurement of the time period is inversely proportional to the number of vibrations measured. So, if the student measures the time for 100 vibrations instead of 10 vibrations, the relative error will be reduced by a factor of 10.

To find the percentage reduction, We can calculate:

Percentage reduction :

• = (Initial error - Final error) / Initial error * 100%

Since the error is reduced by a factor of 10:

Percentage reduction :

• = (1 - 1/10) / 1 * 100% = 90%

So, the relative error in the measurement of the time period will be reduced by 90%, which corresponds to option (d).