A particle executes simple harmonic motion under the restoring fo… - Vidyadip

MCQ

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will:

A
Remain $T$
B
Become $2T$
C
Become $\frac{\text{T}}{2}$
✓
Become $\frac{\text{T}}{\sqrt{2}}$

✓

Answer

Correct option: D.

Become $\frac{\text{T}}{\sqrt{2}}$

Time period $(T)$ is given by,
$\text{T}=2\pi\sqrt{\frac{\text{m}}{\text{k}}}$
where $m$ is the mass, and $k$ is spring constant.
When the spring is divided into two parts, the new spring constant $k_1$ is given as,
$\text{k}_1=2\text{k}$
New time period $T_1$:
$\text{T}_1=2\pi\sqrt{\frac{\text{m}}{2\text{k}}}=\frac{1}{\sqrt{2}}2\pi\sqrt{\frac{\text{m}}{\text{k}}}=\frac{1}{\sqrt{2}}\text{T}$

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