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A horizontal spring block system executes S.H.M. with amplitude $$A=10\ cm$$, initial phase $$\phi=0$$ and angular frequency $$\omega$$. The mass of block is $$M=13\ kg$$ and there is no friction between the block and the horizontal surface. The spring constant being $$2500\ N/m$$.
At $$t=t_{1}sec$$ [for which $$\omega t_{1}=\phi_{1}=30^{o}$$]. A mass $$m=12\ kg$$ is gently put on the block. [Assume that collision between the block and the mass is perfectly inelastic and mass $$m$$ remains stationary w.r.t. the block $$M$$ always].
Read above passage carefully and answer the following question:
The new angular frequency of the system will be:
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Correct option is A. $$10\ rad/sec$$
Angular frequency $$\omega=\sqrt{\dfrac{k}{m}}$$when new block gets attached with previous one $$m_f=m_1+m_2$$$$m_f=13+12=25\,kg$$
$$\omega_f=\sqrt{\dfrac{k}{m_f}}$$
$$\omega_f=\sqrt{\dfrac{2500}{25}}$$
$$\omega_f=\sqrt{100}$$
$$\omega_f=10\,rad/s$$
$$\omega_f=\sqrt{\dfrac{k}{m_f}}$$
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