Assuming all pulleys, springs and string massless. Consider all s… - Vidyadip

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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