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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