Question

A quartz vein in a granitic outcrop has an initial length of 20 cm. If it undergoes uniform stretching resulting in a longitudinal strain of 0.45, the length of the vein post deformation is _________cm (answer in integer).

Hint:

Final length equals initial length multiplied by (1 + strain).

Answer 1

Correct Answer: 29

Step 1: Recall the definition of longitudinal strain.
Longitudinal strain, also called extension, compares the change in length of an object to its original length. It is written as
\[ e = \frac{L_f - L_i}{L_i} \]
where \(L_i\) is the original, undeformed length and \(L_f\) is the final, deformed length.

Step 2: Note down the given values.
\[ L_i = 20 \text{ cm}, \quad e = 0.45 \]

Step 3: Rearrange for the final length.
\[ L_f = L_i(1 + e) \]

Step 4: Substitute and calculate.
\[ L_f = 20 \times (1 + 0.45) = 20 \times 1.45 \]
\[ L_f = 29 \text{ cm} \]

Step 5: Final answer.
After the uniform stretching, the quartz vein grows from 20 cm to 29 cm.
\[ \boxed{L_f = 29 \text{ cm}} \]