Question

The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

• A. $\frac{T}{4}$
• B. $T$
• C. $2T$
• D. $\frac{T}{2}$

Answer 1

The correct option is D $\frac{T}{2}$

Given:
Initial time period $=T$

Time period for spring is given by

$T=2\pi \sqrt{\frac{m}{k}}$
When the spring is cut into four equal parts, the spring constant of one part will becomes $4k$,

$\Rightarrow k^{\prime }=4k$
Therefore the new time period will become
$T^{\prime }=2\pi \sqrt{\frac{m}{k^{\prime }}}$
$T^{\prime }=2\pi \sqrt{\frac{m}{4k}}$
$\Rightarrow T^{\prime }=\frac{T}{2}$

Hence, option $\left(C\right)$ is correct.