Question 295: Properties of Matter

Question

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

Accepted Answer

Let initial length and diameter be l
1
and d
1
, whereas final length and diameter be l
2
and d
2
.
Given, l
2
= 2l
1
, d
2
= 2d
1
, $$\Delta$$l
1
= 0.04 m
By using formula of Young's modulus of elasticity,
$$Y = {{F\,.\,l} \over {A\Delta l}}$$
$$	herefore$$ $${Y_1} = {Y_2}$$
$$ \Rightarrow {{F{l_1}} \over {{A_1} 	imes \Delta {l_1}}} = {{F{l_2}} \over {{A_2} 	imes \Delta {l_2}}}$$
$$ \Rightarrow {{F{l_1}} \over {\pi {{({d_1}/2)}^2} 	imes 0.04}} = {{F2{l_1}} \over {\pi {{(2{d_1}/2)}^2} 	imes \Delta {l_2}}}$$
$$ \Rightarrow {1 \over {1/4 	imes 0.04}} = {2 \over {\Delta {l_2}}}$$
$$ \Rightarrow \Delta {l_2} = 0.02$$ m = 2 cm

Properties of Matter

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

Choose the correct answer: