1. Time period of a mass-spring system

   For a spring of force constant $k$ attached to a mass $m$, the time period is $T = 2\pi\sqrt{\frac{m}{k}}.$

2. Effect of cutting the spring into $n$ equal parts

   The spring constant of a spring is inversely proportional to its length: $k \propto \frac{1}{L}.$

   If the original spring of length $L$ is cut into $n$ equal parts, each part has length $\frac{L}{n}.$

   Therefore, the spring constant of each part becomes $k' = nk.$

3. New time period for each part

   Using the same mass $m$, the time period of one part is $T' = 2\pi\sqrt{\frac{m}{k'}} = 2\pi\sqrt{\frac{m}{nk}}.$

   Since $T = 2\pi\sqrt{\frac{m}{k}},$ we get $T' = \frac{T}{\sqrt{n}}.$

4. Option check

   • A: $T\sqrt n$ ❌
   • B: $T/\sqrt n$ ✅
   • C: $nT$ ❌
   • D: $T$ ❌

Therefore, the correct answer is Option B.