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વાહનની છત પર $L$ લંબાઇનું લોલક લટકાવેલ છે. વાહન ઘર્ષણરહિત $\alpha$ ખૂણો ઘરાવતા ઢાળ પર સરકતુ હોય તો તેનો આવર્તકાળ કેટલો થાય?
$ 2\pi \sqrt {\frac{L}{{g\cos \alpha }}} $
$ 2\pi \sqrt {\frac{L}{{g\sin \alpha }}} $
$ 2\pi \sqrt {\frac{L}{g}} $
$ 2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $
Solution
(a) See the following force diagram. Vehicle is moving down the frictionless inclined surface so, it's acceleration is $g\sin \theta $. Since vehicle is accelerating, a pseudo force $m(g\sin \theta )$ will act on bob of pendulum which cancel the $\sin \theta $ component of weight of the bob.
Hence net force on the bob is $F_{net} = mg\cos \theta $ or net acceleration of the bob is ${g_{eff}} = g\cos \theta $
$\therefore $ Time period $T = 2\pi \sqrt {\frac{l}{{{g_{eff}}}}} = 2\pi \sqrt {\frac{l}{{g\cos \theta }}} $
