Question

The time period of 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. T/4
• B. T
• C. T/2
• D. 2T

Answer 1

Answer: (C)

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