Question

If 3×10-3j of work is done in stretching a wire through 1mm the workdone in stretching it through 3mm is

Answer 1

Given:

3 × 10^(-3) J of work is done in stretching a wire by 1 mm.

To find:

Work done in stretching the wire by 3mm.

Calculation:

Considering the wire to have spring like effect and the spring constant be k , we can say :

$\boxed{ \sf{work = \dfrac{1}{2} k {x}^{2} }}$

In the 1st case :

$\sf{work = \dfrac{1}{2} k {x}^{2} }$

$\sf{ = >3 \times {10}^{ - 3} = \dfrac{1}{2} k {(1)}^{2} }$

$\sf{ = >3 \times {10}^{ - 3} = \dfrac{k}{2} }$

In the 2nd case:

$\sf{work = \dfrac{1}{2} k {x}^{2} }$

$\sf{ = > work = \dfrac{1}{2} k {(3)}^{2} }$

$\sf{ = > work = \dfrac{1}{2} k \times 9 }$

$\sf{ = > work = 3 \times {10}^{ - 3} \times 9 }$

$\sf{ = > work = 27 \times {10}^{ - 3} \: joule }$

So final answer is:

$\boxed{\rm{work = 27 \times {10}^{ - 3} \: joule }}$