Step 1: Recall the working principle of a strain gauge.
When a strain gauge is stretched or compressed, its electrical resistance changes.
Step 2: Identify the operating principle.
The applied force produces strain, which changes the resistance of the strain gauge.
Thus,
\[
\boxed{\text{Force measurement is based on the change in resistance due to strain.}}
\]
Hence,
\[
\boxed{(C)}
\]
is the correct answer.