A particle of mass $5 \mathrm{~g}$ is executing S.H.M. with an amplitude $0.3 \mathrm{~m}$ and period…

A particle of mass $5 \mathrm{~g}$ is executing S.H.M. with an amplitude $0.3 \mathrm{~m}$ and period $\frac{\pi}{5} \mathrm{~s}$. The maximum value of the force acting on the particle is
  1. $0.15 \mathrm{~N}$
  2. $4 \mathrm{~N}$
  3. $5 \mathrm{~N}$
  4. $0.3 \mathrm{~N}$

Solution

$\begin{aligned} & \mathrm{m}=5 \mathrm{~g}=5 \times 10^{-3} \mathrm{~kg}, \mathrm{~A}=0.3 \mathrm{~m}, \mathrm{~T}=\frac{\pi}{5} \mathrm{~s} \\ & \omega=\frac{2 \pi}{\mathrm{T}}=10 \mathrm{rad} / \mathrm{s} \end{aligned}$ Maximum force, $\mathrm{F}=\mathrm{m} \omega^2 \mathrm{~A}=5 \times 10^{-3} \times(10)^2 \times 0.3=0.15 \mathrm{~N}$ :

Asked in: MHT CET 2021 (20 Sep Shift 2)

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