SATHEE: Simple Harmonic Motion 3 Question 6

Simple Harmonic Motion 3 Question 6

6. The period of oscillation of simple pendulum of length $L$ suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination $α$ , is given by

(a) $2 π \sqrt{\frac{L}{g \cos α}}$

(b) $2 π \sqrt{\frac{L}{g \sin α}}$

(d) $2 π \sqrt{\frac{L}{g \tan α}}$

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Answer:

Correct Answer: 6. (a)

Solution:

Free body diagram of bob of the pendulum with respect to the accelerating frame of reference is as follows

$∴$ Net force on the bob is $F_{net} = m g \cos α$ or net acceleration of the bob is $g_{eff} = g \cos α$

$T = 2 π \sqrt{\frac{L}{g_{eff}}}$

NOTE

Whenever point of suspension is accelerating

$Take, T = 2 π \sqrt{\frac{L}{g_{eff}}}$

where, $g_{eff} = g - a$

$a =$ acceleration of point of suspension.

In this question, $a = g \sin α$ (down the plane)

$\begin{aligned} | g - a | = g_{eff} \\ = \sqrt{g^{2} + (g \sin α)^{2} + 2 (g) (g \sin α) \cos (90^{\circ} + α)} \\ = g \cos α \end{aligned}$

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Simple Harmonic Motion 3 Question 6

6. The period of oscillation of simple pendulum of length $L$ suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination $α$ , is given by

Answer:

NOTE

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Simple Harmonic Motion 3 Question 6

6. The period of oscillation of simple pendulum of length L suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination α, is given by

Answer:

NOTE

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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6. The period of oscillation of simple pendulum of length $L$ suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination $α$ , is given by