Question 136: Properties of Matter

Question

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y
1
and Y
2
. The combination behaves as a single wire then its Young's modulus is :

Accepted Answer

In series combination $$\Delta$$l = l
1
+ l
2
$$Y = {{F/A} \over {\Delta l/l}} \Rightarrow \Delta l = {{Fl} \over {AY}}$$
$$ \Rightarrow \Delta l \propto {l \over Y}$$
Equivalent length of rod after joining is = 2l
As, lengths are same and force is also same in series
$$\Delta l = \Delta {l_1} + \Delta {l_2}$$
$${{{l_{eq}}} \over {{Y_{eq}}}} = {l \over {{Y_1}}} + {l \over {{Y_2}}} \Rightarrow {{2l} \over Y} = {l \over {{Y_1}}} + {l \over {{Y_2}}}$$
$$	herefore$$ $$Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$

Answer

$$Y = {{2{Y_1}{Y_2}} \over {3({Y_1} + {Y_2})}}$$

Answer

$$Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$

Answer

$$Y = {{{Y_1}{Y_2}} \over {2({Y_1} + {Y_2})}}$$

Answer

$$Y = {{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}$$

Properties of Matter

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y 1 and Y 2 . The combination behaves as a single wire then its Young's modulus is :

Choose the correct answer: