| 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 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, and Statement 2 is the correct explanation for statement 1
D) Statement 1 is true, Statement 2 is true, and Statement 2 is not the correct explanation of Statement 1
Correct Answer: A
Solution :
| [a] \[{{k}_{1}}{{x}_{1}}={{k}_{2}}{{x}_{2}}=F\] |
| \[{{W}_{1}}=\frac{1}{2}\,\,{{k}_{1}}{{x}_{1}}^{2}=\frac{{{({{k}_{1}}{{x}_{1}})}^{2}}}{2{{k}_{1}}}=\frac{{{F}^{2}}}{2{{k}_{1}}}\] |
| 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. |
You need to login to perform this action.
You will be redirected in
3 sec
