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: Read the strain as a percent change.
A longitudinal strain of $0.45$ just means the vein got $45\%$ longer than it started.

Step 2: Find the extra length gained.
The starting length is $20$ cm, so the extra length added is
\[ 0.45 \times 20 = 9 \text{ cm} \]

Step 3: Add the extension to the original length.
\[ L_f = 20 + 9 = 29 \text{ cm} \]

Step 4: Check the answer against the strain formula.
Using $e = (L_f - L_i)/L_i$, putting in $L_f = 29$ and $L_i = 20$ gives $e = 9/20 = 0.45$, which matches the value given in the question.
\[ \boxed{L_f = 29 \text{ cm}} \]