A wire of length and radius is clamped rigidly at one end. When the other end of the wire is pulled by a force , its length increases by . Another wire of the same material of length and radius is pulled by a force . Then the increase in its length w

Question

A wire of length $' L'$ and radius $' r'$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$ , its length increases by $' l'$ .

Another wire of the same material of length $' 2 L'$ and radius $' 2 r'$ is pulled by a force $' 2 f'$ . Then the increase in its length will be: [2023]

Smart Achievers · Accepted Answer

(2)

$\frac{f}{π r^{2}} = Y \frac{ℓ}{L}$

$\frac{2 f}{π {(2 r)}^{2}} = Y \frac{ℓ'}{2 L}$

$\Rightarrow \frac{2}{1} = \frac{2 ℓ'}{ℓ} \Rightarrow ℓ' = ℓ$

Solution

1 $2 l$

2 $l$

3 $4 l$

4 $\frac{l}{2}$

Ans.
(2)

$\frac{f}{π r^{2}} = Y \frac{ℓ}{L}$

$\frac{2 f}{π {(2 r)}^{2}} = Y \frac{ℓ'}{2 L}$

$\Rightarrow \frac{2}{1} = \frac{2 ℓ'}{ℓ} \Rightarrow ℓ' = ℓ$

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Solution

Q. A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by 'l'. Another wire of the same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will be: [2023]

1 2l

2 l

3 4l

4 l2