The point A moves with a uniform speed along the circumference

Question:

The point A moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{~m}$ and covers $30^{\circ}$ in $0.1 \mathrm{~s}$. The perpendicular projection ' $\mathrm{P}$ ' from 'A' on the diameter $\mathrm{MN}$ represents the simple harmonic motion of ' $P$ '. The restoration force per unit mass when $P$ touches $M$ will be :

  1. $100 \mathrm{~N}$

  2. $0.49 \mathrm{~N}$

  3. $50 \mathrm{~N}$

  4. $9.87 \mathrm{~N}$


Correct Option: , 4

Solution:

$30^{\circ} \rightarrow 0.1 \mathrm{~s}$

$360^{\circ} \rightarrow 1.2 \mathrm{~s}=\mathrm{T}$

$\omega=\frac{2 \pi}{T}=\frac{5 \pi}{3}$

At $\mathrm{M}, \mathrm{F}=\mathrm{m} \omega^{2} \mathrm{~A} \Rightarrow \frac{\mathrm{F}}{\mathrm{m}}=\omega^{2} \mathrm{~A}$

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