An object suspended from a spring exhibits oscillations of period T. Now, the spring is cut in two halves and the same object is suspended with two halves as shown in the figure. The new time period of oscillation will become

Options

A. `(T)/(2 sqrt(2))`
B. `(T)/(2)`
C. `(T)/(sqrt(2))`
D. 2T

Answer

B

Explanation

Let k be the spring constant of each half part of the spring. For a complete spring, the spring constant `k' = k//2` (spring in series). When two splitted parts of a spring are connected to the body, then spring are in parallel. Their effective spring constant, `k' = k + k = 2k`.
`because" "T = 2pi sqrt((m)/(k))rArr T prop (1)/(sqrt(k))" "("for a fixed value of m")`
`therefore" "(T')/(T)=sqrt((k//2)/(2k))=(1)/(2) or T'=(T)/(2)`