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STD 11 - 13. oscillations — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 13. oscillations4 Marks
MCQ
Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$
  • A
    The angular frequency for small oscillation of the system is $\sqrt \frac{K}{3m}$
  • ✓
    The angular frequency for small oscillation of the system is $\sqrt \frac{4K}{33m}$
  • C
    The elastic potential energy of system at equilibrium is $\frac{33m^2g^2}{4K}$
  • D
    The elastic potential energy of system at equilibrium is $\frac{3m^2g^2}{2K}$
✓

Answer

Correct option: B.
The angular frequency for small oscillation of the system is $\sqrt \frac{4K}{33m}$
b
$x=\frac{y_{1}}{2}+2 y_{2}+2 y_{3}$       $...(1)$

$\Delta \mathrm{T}=\mathrm{ma}$       $...(2)$

$2 \Delta \mathrm{T}=\mathrm{Ky}_{2}$           $...(3)$

$2 \Delta \mathrm{T}=\mathrm{Ky}_{3}$           $...(4)$

$\frac{\Delta \mathrm{T}}{2}=\mathrm{Ky}_{1}$           $...(5)$

Solving eqn.

$x=\Delta T\left(\frac{33}{4 K}\right)$

$w^{2}=\left(\frac{4 K}{33}\right)$

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