SATHEE: Simple Harmonic Motion 1 Question 1

Simple Harmonic Motion 1 Question 1

1. A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_{1}$ . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_{2}$ . Then

(2019 Main, 11 Jan III)

(a) $K_{2} = 2 K_{1}$

(b) $K_{2} = \frac{K_{1}}{2}$

(d) $K_{2} = K_{1}$

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Answer:

Correct Answer: 1. (b)

Solution:

Kinetic energy of a pendulum is maximum at its mean position. Also, maximum kinetic energy of pendulum

$K_{max} = \frac{1}{2} m ω^{2} a^{2}$

where,angular frequency

$\begin{aligned} ω & = \frac{2 π}{T} = \frac{2 π}{2 π \sqrt{\frac{l}{g}}} \\ or ω & = \sqrt{\frac{g}{l}} or ω^{2} = \frac{g}{l} \end{aligned}$

and $a =$ amplitude.

As amplitude is same in both cases so;

$\begin{aligned} K_{max} \propto ω^{2} \\ K_{max} \propto \frac{1}{l} \end{aligned}$

$[∵ g$ is constant $]$

According to given data, $K_{1} \propto \frac{1}{l}$

$\begin{array}{ll} and & K_{2} \propto \frac{1}{2 l} \\ ∴ & \frac{K_{1}}{K_{2}} = \frac{1 / l}{1 / 2 l} = 2 \\ or & K_{1} = 2 K_{2} \Rightarrow K_{2} = \frac{K_{1}}{2} \end{array}$

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Simple Harmonic Motion 1 Question 1

1. A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_{1}$ . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_{2}$ . Then

Answer:

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परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Simple Harmonic Motion 1 Question 1

1. A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2. Then

Answer:

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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1. A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_{1}$ . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_{2}$ . Then