The force constant of an oscillating simple pendulum is

The force constant of an oscillating simple pendulum is
  1. Independent of mass of the bob as well as length of the pendulum
  2. Inversely proportional to mass of the bob and length of the pendulum
  3. Directly proportional to the mass of the bob
  4. Directly proportional to length of the bob

Solution

For a simple pendulum, restoring torque equates the $\begin{aligned} & \tau=-m g L \sin \theta=I \alpha \\ & \Rightarrow \alpha=-\frac{m g L}{m L^2} \sin \theta \approx-\frac{g}{L} \theta \\ & \alpha \approx-\left(\frac{g}{L}\right) \theta \Rightarrow \alpha=-\omega^2 \theta=-\left(\frac{g}{L}\right) \theta \end{aligned}$ Force constant of an oscillating simple pendulum is given by $k=m \omega^2$ $k \propto m$ and $k \propto \omega^2=\left(\frac{g}{L}\right)$ Therefore, force constant of an oscillating simple pendulum is directly proportional to the mass of the bob.

Asked in: MHT CET 2022 (11 Aug Shift 1)

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