JEE MAIN - Physics (2002 - No. 39)
If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be
$$T\sqrt n $$
$$T/\sqrt n $$
$$nT$$
$$T$$
설명
Let the spring constant of the original spring be $$k.$$
Then its time period $$T = 2\pi \sqrt {{m \over k}} $$ where $$m$$ is the mass of oscillating body.
When the spring is cut into $$n$$ equal parts, the spring constant of one part becomes $$nk.$$ Therefore the new time period,
$$T' = 2\pi \sqrt {{m \over {nk}}} = {T \over {\sqrt n }}$$
Then its time period $$T = 2\pi \sqrt {{m \over k}} $$ where $$m$$ is the mass of oscillating body.
When the spring is cut into $$n$$ equal parts, the spring constant of one part becomes $$nk.$$ Therefore the new time period,
$$T' = 2\pi \sqrt {{m \over {nk}}} = {T \over {\sqrt n }}$$