Question

If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will be:

• A. $T\sqrt{n}$
• B. $\frac{T}{\sqrt{n}}$
• C. $nT$
• D. $T$

Answer 1

Answer: (B)

$\frac{T}{\sqrt{n}}$

Initial length = L

Initial spring constant = K

$T\propto \frac{1}{\sqrt{K}}\to \left(i\right)$

Now length = L/n

We know that :-

$K\times L=K^{\prime }\times \frac{L}{n}$

$K^{\prime }=kn$

so, $T^{\prime }\propto \frac{1}{\sqrt{Kn}}\to \left(ii\right)$

$\frac{T}{T^{\prime }}=\sqrt{n}$

$T^{\prime }=T/\sqrt{n}$

Option (B)