This question has statement $1$ and statement $2$. Of the four choices given after the statements, choose…

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 $\mathrm{S_1}$ and $\mathrm{S_2}$ 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 $\mathrm{S_1}$ than on spring $\mathrm{S_2}$. Statement $1$ : If stretched by the same amount, work done on $\mathrm{S}_1$, will be more than that on $\mathrm{S}_2$ Statement $2: k_1 < k_2$
  1. Statement $1$ is false, Statement $2$ is true
  2. Statement $1$ is true, Statement $2$ is false
  3. Statement $1$ is true, Statement $2$ is the correct explanation for statement $1$
  4. Statement $1$ is true, Statement $2$ is true, Statement $2$ is not the correct explanation for statement $1$.

Solution

$\mathrm{F}=\mathrm{K}_1 \mathrm{S}_1=\mathrm{K}_2 \mathrm{S}_2$ $\mathrm{W}_1=\mathrm{FS}_1, \mathrm{~W}_2=\mathrm{FS}_2$ $\mathrm{K}_1 \mathrm{S}_1{ }^2>\mathrm{K}_2 \mathrm{S}_2^2$ $\mathrm{S}_1>\mathrm{S}_2$ $\mathrm{K}_1 < \mathrm{K}_2$ $\mathrm{W} \propto \mathrm{K}$ $\mathrm{W}_1 < \mathrm{W}_2$

Asked in: JEE Main 2012 (Offline)

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