SATHEE: Laws of Motion 4 Question 2

Laws of Motion 4 Question 2

2. A particle is moving along a circular path with a constant speed of $10 m s^{- 1}$ . What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{\circ}$ around the centre of the circle?

(2019 Main, 11 Jan I)

(a) $10 \sqrt{2} m / s$

(b) $10 m / s$

(d) Zero

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Answer:

Correct Answer: 2. (b)

Solution:

Let $v_{1}$ be the velocity of the particle moving along the circular path initially, $v_{1}$ and $v_{2}$ be the velocity when it moves through an angle of $60^{\circ}$ as shown below.

From the figure,

$\begin{aligned} Δ v & = v_{2} - v_{1} \\ \Rightarrow | Δ v | & = 2 v \sin \frac{θ}{2} = 2 v \sin 30^{\circ} [∵ | v_{1} | = | v_{2} |] \\ = 2 v \times \frac{1}{2} = v (Given, v = 10 m / s) \\ \Rightarrow | Δ v | & = 10 m / s \end{aligned}$

Alternate method

$∵ Δ v = v_{2} - v_{1} = v_{2} + (- v_{1})$

$∴ | Δ v |^{2} = v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} \cos 120^{\circ}$

$= v^{2} + v^{2} + 2 v \times v \times - \frac{1}{2}$

$\Rightarrow | Δ v | = v = 10 m / s$ .

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Laws of Motion 4 Question 2

2. A particle is moving along a circular path with a constant speed of $10 m s^{- 1}$ . What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{\circ}$ around the centre of the circle?

Answer:

Alternate method

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Laws of Motion 4 Question 2

2. A particle is moving along a circular path with a constant speed of 10ms−1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle?

Answer:

Alternate method

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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2. A particle is moving along a circular path with a constant speed of $10 m s^{- 1}$ . What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{\circ}$ around the centre of the circle?