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JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    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 \[{{S}_{1}}\] and \[{{S}_{2}}\] of force constants \[{{k}_{1}}\]and \[{{k}_{2}}\], respectively, are stretched by the same force, it is found that more work is done on spring \[{{S}_{1}}\] than on spring \[{{S}_{2}}\]. Statement 1: If stretched by the same amount, work done on \[{{S}_{1}}\], will be more than that on \[{{S}_{2}}\]Statement 2:  \[{{k}_{1}}<{{k}_{2}}\]   AIEEE  Solved  Paper-2012

    A) Statement 1 is false, Statement 2 is true.

    B) Statement 1 is true, Statement 2 is false

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

    D) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

    Correct Answer: A

    Solution :

                 \[{{k}_{1}}{{x}_{1}}={{k}_{2}}{{x}_{2}}=F\] \[{{W}_{1}}=\frac{1}{2}\,\,{{k}_{1}}{{x}_{1}}^{2}=\frac{{{({{k}_{1}}{{x}_{1}})}^{2}}}{2{{k}_{1}}}=\frac{{{F}^{2}}}{2{{k}_{1}}}\] Similarly \[{{W}_{2}}=\frac{{{F}^{2}}}{2{{k}_{2}}}\]               \[\Rightarrow \]               \[W\propto \frac{1}{k}\] \[{{W}_{1}}>{{W}_{2}}\]                   \[\Rightarrow {{k}_{1}}<{{k}_{2}}\] statement-2 is true.              Statement-1          \[{{W}_{1}}=\frac{1}{2}{{k}_{1}}\,{{x}^{2}}\]                                    \[{{W}_{2}}=\frac{1}{2}{{k}_{1}}\,{{x}^{2}}\] So , \[{{W}_{2}}>{{W}_{1}}\] Statement-1 is false.


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