Question 324: Properties of Matter

Question

Two wires are made of the same material and
have the same volume. The first wire has
cross-sectional area A and the second wire has
cross-sectional area 3A. If the length of the first
wire is increased by $$\Delta $$l on applying a force F,
how much force is needed to stretch the second
wire by the same amount?

Accepted Answer

Let the wire 1 is of length = l and wire 2 of
length = $${l \over 3}$$
Now area of wire 1 = A while area of wire 2 = 3A
For wire 1,
$$\Delta $$l = $$\left( {{F \over {AY}}} \right)l$$ ....(i)
For wire 2, let F' force is applied
$$\Delta $$l = $$\left( {{{F'} \over {3AY}}} \right){l \over 3}$$ ....(2)
From equation (i) & (ii)
$$\left( {{F \over {AY}}} \right)l$$ = $$\left( {{{F'} \over {3AY}}} \right){l \over 3}$$
$$ \Rightarrow $$ F' = 9F

Answer

6F

Answer

F

Answer

9F

Answer

4F

Properties of Matter

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