A) \[\frac{T}{2}\]
B) 2T
C) \[\frac{T}{4}\]
D) T
Correct Answer: A
Solution :
| Key Idea: Force constant of spring is inversely proportional to length of spring. |
| Time period of mass suspended from spring. |
| \[T=2\pi \sqrt{\frac{m}{k}}\] (i) |
| Now we know that, |
| spring constant \[\propto \frac{1}{\text{length}}\] |
| or \[k\propto \frac{1}{x}\] ...(ii) |
| Since, spring is cut into four equal parts, hence force constant of each part becomes four times the previous. So, |
| \[k'=4k\] |
| So, new time period of same mass suspended from one of the parts, |
| \[T'=2\pi \sqrt{\frac{m}{4k}}=\frac{1}{2}.2\pi \sqrt{\frac{m}{k}}=\frac{T}{2}\] |
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