Verified Solution • 2025–26 Session moderate

QJEEM22Ph9628: JEE Main 2022 Physics - Class 11 JEEM22Ph9628 Solution: The time period of oscillation of a simple pendulum of length L …

The time 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 α\alpha , is given by :

Multiple Choice Options

  • A 2πL/(gcos⁡α)2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \cos \alpha)}
  • B 2πL/(gsin⁡α)2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \sin \alpha)}
  • C 2πL/g2 \pi \sqrt{\mathrm{L} / \mathrm{g}}
  • D 2πL/(gtan⁡α)2 \pi \sqrt{\mathrm{L} /(\mathrm{g} \tan \alpha)}

Step-by-Step Verified Solution

∣geff∣=∣g‾−a‾∣\left| {{g_{eff}}} \right| = \left| {\overline g - \overline a } \right|

⇒geff=gcos⁡θ\Rightarrow {g_{eff}} = g\cos \theta

⇒T=2πlgeff\Rightarrow T = 2\pi \sqrt {{l \over {{g_{eff}}}}}

=2π=Lgcos⁡θ= 2\pi = \sqrt {{L \over {g\cos \theta }}}

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