The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4 \mathrm{~ms}^{-1}$. The…

The maximum velocity of a particle, executing S.H.M. with an amplitude 7 mm is $4.4 \mathrm{~ms}^{-1}$. The period of oscillation is $\left[\pi=\frac{22}{7}\right]$.
  1. 100 s
  2. 10 s
  3. 0.1 s
  4. $\quad 0.01 \mathrm{~s}$

Solution

$\begin{array}{ll} & \mathrm{V}_{\max }=\mathrm{A} \omega \\ \therefore \quad & 4.4=7 \times 10^{-3}\left(\frac{2 \pi}{\mathrm{~T}}\right) \\ \therefore \quad & \mathrm{T}=\frac{7 \times 10^{-3} \times 2 \times 22}{4.4 \times 7}=0.01 \mathrm{~s} \end{array}$ $\begin{aligned} & \frac{mv^2}{r}= \frac{G M m}{r^2} \\ & v=\sqrt{\frac{G M}{r}} \\ & L=m v r \\ &=m \sqrt{\frac{G M}{r}} r \\ &=m(G M r)^{1 / 2} \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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