Linear measurements with a tape: identify the incorrect statement Consider the following statements about tape measurements and associated corrections. Which one is incorrect?

Introduction / Context:
Tape measurements are influenced by instrumental and environmental factors such as standard length error, temperature, pull, and sag. Recognizing the sign and sense of each correction prevents systematic bias in linear surveying work.

Given Data / Assumptions:

• Standard (nominal) tape length = 100 m; actual length may differ slightly.
• Temperature changes cause thermal expansion or contraction of the tape.
• Sag in unsupported spans makes the taped path longer than the straight chord.
• Steel modulus and geometry govern elastic extension under pull.

Concept / Approach:

Each effect has a predictable correction. If the tape is longer than nominal, recorded measurements are too small and must be increased. Thermal expansion similarly makes the scale longer; readings are again too small and must be increased, not decreased. Sag increases the path length; the correction is subtractive from the measured value to obtain the straight distance. Elastic stretch under a moderate pull of about 5 kg for the given cross-section produces roughly 10 mm extension over 100 m, a reasonable engineering approximation.

Step-by-Step Solution:

Verification / Alternative check:

Thermal correction formula: C_T = α (T − T_0) * L_meas, added when T > T_0, confirms that measured values must be increased, not decreased.

Why Other Options Are Wrong:

A, C, and D state standard, correct relationships; E (“None”) is invalid because B is incorrect.

Common Pitfalls:

Reversing the sign of temperature or standard length correction; forgetting that sag correction is always subtractive; mixing SI and practical units for elasticity computations.

Final Answer:

An increase in temperature lengthens a tape, so the measured distance becomes too large.