The period of oscillation of a simple pendulum of length \(l\) suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination \(\alpha\), is given by

• Correct answer
  A

  \(2 \pi \sqrt{\frac{1}{g \cos \alpha}}\)
• B

  \(2 \pi \sqrt{\frac{1}{g \sin \alpha}}\)
• C

  \(2 \pi \sqrt{\frac{1}{g}}\)
• D

  \(2 \pi \sqrt{\frac{1}{\mathrm{~g} \tan \alpha}}\)

Solution

Hints:
\(\begin{aligned} & \mathrm{g}_{\text {eff }}=\mathrm{g} \cos \alpha \\ & \mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}_{\text {eff }}}} \end{aligned}\)

Hence, the correct answer is option: 'A'.