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  • This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs S1 and S2 of force constants k1 and k2 , respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2.                                                       

Statement 1 : If stretched by the same amount, work done on S1, will be more than that on S2.  

Statement 2 : k1 < k2

 
Option: 1

Statement 1 is false, Statement 2 is true


Option: 2

Statement 1 is true, Statement 2 is false


Option: 3

Statement 1 is true, Statement 2 is the correct explanation for statement 1


Option: 4

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.


Answers (1)

best_answer

For the same force, F=k_{1}x_{1}=k_{2}x_{2}..........(i)

Work done on spring S_{1}  is

W_{1}=\frac{1}{2}k_{1}x_{1}^{2}=\frac{(k_{1}x_{1})^{2}}{2k_{1}}=\frac{F^{2}}{2k_{1}}.........(Using(i))

Work done on spring S_{2} is

W_{2}=\frac{1}{2}k_{2}x_{2}^{2}=\frac{(k_{2}x_{2})^{2}}{2k_{2}}=\frac{F^{2}}{2k_{2}}.........(Using(i))

\therefore \; \; \; \frac{W_{1}}{W_{2}}=\frac{k_{2}}{k_{1}}

As W_{1}> W_{2}\; \; \; \therefore \; \; k_{2}> k_{1}\; or\; k_{1}< k_{2}

Statement 2 is true.

For\; the \; same\; extension,x_{1}=x_{2}=x..........(ii)

Work done on spring S_{1} is

W_{1}=\frac{1}{2}k_{1}x_{1}^{2}=\frac{1}{2}k_{1}x^{2}........(Using\: (ii))

Work done on spring S_{2} is

W_{2}=\frac{1}{2}k_{2}x_{2}^{2}=\frac{1}{2}k_{2}x^{2}........(Using\: (ii))

\therefore \; \; \frac{W_{1}}{W_{2}}=\frac{k_{1}}{k_{2}}

As\; \; k_{1}< k_{2}\; \; \therefore \; \; W_{1}< W_{2}

Statement 1 is false.

 

Posted by

rishi.raj

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