Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio 1 : 3 and the some mass is attached to the longer part, the new time period will be :

Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio 1 : 3 and the some mass is attached to the longer part, the new time period will be :

A
$\sqrt{\frac{3}{2}} T$
B
$\frac{T}{\sqrt{3}}$
C
$\frac{\sqrt{3} T}{2}$
D
$\sqrt{3} T$

Solution:

For spring kl= constant so spring constant of longer part $k' = \frac{4}{3} k .$
But $T \propto \frac{1}{\sqrt{k}} so T' = \frac{\sqrt{3}}{2} T .$

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