Introduction:
In this problem, we are given the length of a pendulum, the time for 100 oscillations, and the accuracy of the measurements. We need to determine the error in the measurement of the acceleration due to gravity (g) caused by the given uncertainties.

Formula:
The formula used to calculate the acceleration due to gravity (g) using the length of a pendulum (L) and the time period (T) for one oscillation is given by:

g = (4π²L) / T²

Given Data:
- Length of pendulum (L) = 20 cm
- Accuracy of length measurement = 0.1 mm
- Time for 100 oscillations (T) = 90 seconds
- Resolution of wristwatch = 1 second

Calculating the error in length measurement:
The accuracy of the length measurement is given as 0.1 mm, which is equivalent to 0.01 cm. Since the pendulum length is given as 20 cm, the relative error in the length measurement can be calculated as:

Relative Error = (0.01 cm) / (20 cm) = 0.0005

Calculating the error in time measurement:
The resolution of the wristwatch is given as 1 second. Since the time for 100 oscillations is measured, the resolution error can be calculated as:

Resolution Error = (1 second) / (100 oscillations) = 0.01 seconds

Calculating the error in acceleration due to gravity:
Using the formula for acceleration due to gravity and the relative errors in length and time measurements, the error in g can be calculated as:

Error in g = (dg/dL) * ΔL + (dg/dT) * ΔT

Where:
(dg/dL) is the partial derivative of g with respect to L
(dg/dT) is the partial derivative of g with respect to T
ΔL is the relative error in length measurement
ΔT is the resolution error in time measurement

By calculating the partial derivatives of g with respect to L and T, and substituting the given values, we can find the error in g. However, without the actual values of the partial derivatives, we cannot provide a specific numerical answer for the error in g.

Del t/t=del g/2g+del l/l