MCQ
The ratio of the lengths of two wires $A$ and $B$ of same material is $1 : 2$ and the ratio of their diameter is $2 : 1.$ They are stretched by the same force, then the ratio of increase in length will be
- A$2:1$
- B$1:4$
- ✓$1:8$
- D$8:1$
✓
Answer
Correct option: C.
$1:8$
c
(c) $l = \frac{{FL}}{{AY}} \Rightarrow l \propto \frac{L}{{{d^2}}}$==>$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}} \times {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2}$
(c) $l = \frac{{FL}}{{AY}} \Rightarrow l \propto \frac{L}{{{d^2}}}$==>$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}} \times {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2}$
$ = \frac{1}{2} \times {\left( {\frac{1}{2}} \right)^2} = \frac{1}{8}$
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