Question

Spring of spring constant $k$ is cut into $n$ equal parts, out of which are parts $r$ placed in parallel and connected with mass $M$ as shown in figure. The time period of oscillatory motion of mass $M$ is:

• A. $T=2\pi \sqrt{\frac{rM}{nK}}$
  
• B. $T=2\pi \sqrt{\frac{nM}{rK}}$
• C. $T=2\pi \sqrt{\frac{nrM}{K}}$
  
• D. $T=2\pi \sqrt{\frac{M}{nrK}}$

Answer 1

The correct option is D $T=2\pi \sqrt{\frac{M}{nrK}}$

We know that, $T=2\pi \sqrt{\frac{M}{K}}$
A spring of spring constant $k$ is cut into an equal parts, so new spring constant will be,
$K=nk$
Now $r$ part are taken in parallel.
$K=nrk$
Time period of oscillation can be expressed as below,
$T=2\pi \sqrt{\frac{M}{K}}$
$T=2\pi \sqrt{\frac{M}{nrK}}$
Final answer: (a)