Question

A take-up motion is shown below. The number of teeth on gear A, B, C, D and E are 60, 20, 40, 25 and 50, respectively. The circumference of the take-up roller is 40 cm. If one tooth is broken on gear B, then the wavelength (cm) of the fault in fabric (in integer) is ______________.

Hint:

Fault wavelength equals fabric length delivered per one full rotation of the faulty gear.

Answer 1

Correct Answer: 10

A broken tooth on gear B creates one disturbance every full rotation of gear B.
Gear B has 20 teeth, so 1 broken tooth produces 1 fault per rotation.
The take-up roller pulls fabric according to its circumference.
Given roller circumference = 40 cm.
Thus, one rotation of gear B corresponds to 40 cm of fabric being wound.
Therefore, the wavelength of the repeating fault is equal to the roller circumference.
\[ \text{Wavelength} = 40 \, \text{cm} \]
Hence, the wavelength in integer form is 40.
Final Answer: 40