Answer:
The work done required is [tex]W_{1}=4W_{2}[/tex]
Explanation:
Given that,
Stretch spring = 2 cm
Stretch spring = 1 cm
We need to calculate the work done
Using formula of work done
[tex]W_{1}=\dfrac{1}{2}kx_{1}^2[/tex]
Put the value into the formula
[tex]W_{1}=\dfrac{1}{2}\timesk\times0.02^2[/tex].....(I)
We need to calculate the work done
Using formula of work done
[tex]W_{2}=\dfrac{1}{2}kx_{2}^2[/tex]
Put the value into the formula
[tex]W_{1}=\dfrac{1}{2}\timesk\times0.01^2[/tex].....(II)
We need to calculate the work done
Using equation (I) and (II)
[tex]\dfrac{W_{1}}{W_{2}}=\dfrac{\dfrac{1}{2}\timesk\times0.02^2}{\dfrac{1}{2}\timesk\times0.01^2}[/tex]
[tex]\dfrac{W_{1}}{W_{2}}=\dfrac{0.02^2}{0.01^2}[/tex]
[tex]W_{1}=4W_{2}[/tex]
Hence, The work done required is [tex]W_{1}=4W_{2}[/tex]
