If two similar spring each of spring constant $\mathrm{K}_{1}$ are joined in series, the new spring constant and time period would be changed by a factor :

(B) $\frac{1}{2}, 2 \sqrt{2}$

(C) $\frac{1}{4}, 2 \sqrt{2}$

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Elasticity & SHM

If two similar spring each of spring constant

K_{1}

are joined in series, the new spring constant and time period would be changed by a factor :

Answer: (A)

Springs in series carry the same force, so their extensions add and the effective constant follows from

\frac{1}{K _{eff}} = \frac{1}{K _{1}} + \frac{1}{K _{1}}

, which gives

K_{eff} = \frac{K _{1}}{2}

: the spring constant falls to half its value. For a mass on a spring

T = 2 π \frac{m}{K}

, so

T \propto \frac{1}{K}

and halving the constant multiplies the period by

2

. The spring constant changes by the factor

\frac{1}{2}

and the time period by the factor

2

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option