Question

The "lead" in pencils is a graphite composition with a Young’s modulus of about 1×1010N/m21×1010⁢N/m2. Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.
a) 0.03 mm
b) 0.1 mm
c) 0.3 mm
d) 1 mm

Answer 1

Answer:

b) 0.1 mm

Explanation:

Given that

E= 1 x 10¹⁰ N/m²

F= 4 N

d= 0.5 mm

L = 60 mm

We know that elongation due to force F given as

$\Delta L=\dfrac{FL}{AE}$

$\Delta L=\dfrac{FL}{\dfrac{\pi d^2}{4}\times E}$

$\Delta L=\dfrac{4\times 60}{\dfrac{\pi \times 0.5^2}{4}\times 10^4}$

ΔL = 0.12 mm

Therefore the answer is -

b) 0.1 mm