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

Options

A. `T=2pisqrt((M)/(rnK))`
B. `T=2pisqrt((nrM)/(K))`
C. `T=2pisqrt((nM)/(nK))`
D. `T=2pisqrt((nM)/(rK))`

Answer

A

Explanation

`K.I=k'xx(I)/(n)` constant
new spring constand for each part is k'=nK
Now r part are taken in parallel.
so `K_(eq)=nrk`, Time period =`2pisqrt((M)/(K_(eq)))=2pisqrt((M)/(nrK))`