P a Particle Executes Simple Harmonic Motion Under the Restoring Force Provided by a Spring. the Time Period is T. - Physics

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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

Options

  • remain T

  • become 2T

  • become T/2

  • become \[T/\sqrt{2}\]

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Solution

become \[T/\sqrt{2}\]

Time period \[\left( T \right)\] is given by,

\[T = 2\pi\sqrt{\frac{m}{k}}\]

where m is the mass, and
          k is spring constant.

When the spring is divided into two parts, the new spring constant k1 is given as,
k1 =\[2k\]

New time period T1 :
T1  = \[2\pi\sqrt{\frac{m}{2k}} = \frac{1}{\sqrt{2}}2\pi\sqrt{\frac{m}{k}} = \frac{1}{\sqrt{2}}T\]

  Is there an error in this question or solution?
Chapter 12: Simple Harmonics Motion - MCQ [Page 251]

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HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 12 Simple Harmonics Motion
MCQ | Q 14 | Page 251

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