Question 120: 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 Y1 and Y2. 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 Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :

Choose the correct answer: