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

Options

A. nT
B. `(T)/(sqrt(n))`
C. `Tsqrt(n)`
D. T

Answer

B

Explanation

Let K be the spring constant of the spring. When it is cut into n equal parts, the spring constant will be K'=nK
`therefore T=2pi sqrt((m)/(K)) and T'=2pi sqrt((m)/(nK))`
`therefore (T')/(T)=sqrt((m)/(nK)xx(K)/(m))= (1)/(sqrt(n))`
`therefore T'=(T)/(sqrt(n))`