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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now
  • A
    $\frac{T}{2}$
  • ✓
    $\frac{T}{\sqrt{2}}$
  • C
    $\sqrt{2}T$
  • D
    $2T$
✓

Answer

Correct option: B.
$\frac{T}{\sqrt{2}}$
b
(b) $T = 2\pi \sqrt {\frac{m}{k}} $. 

Also spring constant $(k) \propto \frac{1}{{{\rm{Length (}}L)}}$, when the spring is half in length, then $k$ becomes twice. 

$\therefore T' = 2\pi \sqrt {\frac{m}{{2k}}} $

$\Rightarrow \frac{{T'}}{T} = \frac{1}{{\sqrt 2 }} $

$\Rightarrow T' = \frac{T}{{\sqrt 2 }}$

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