SATHEE: Centre of Mass 3 Question 10

Centre of Mass 3 Question 10

13. A particle of mass $m$ moving in the $x$ -direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ -direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

(2015 Main)

(a) $50$

(b) $56$

(d) $44$

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Answer:

Correct Answer: 13. (b)

Solution:

In all type of collisions, momentum of the system always remains constant. In perfectly inelastic collision, particles stick together and move with a common velocity.

Let this velocity is $v_{c}$ . Then,

initial momentum of system $=$ final momentum of system

or $m (2 v) \hat{i} + 2 m (v) \hat{j} = (m + 2 m) v_{c}$

$∴ v_{c} = \frac{2}{3} (v \hat{i} + v \hat{j})$

$| v_{c} |$ or $v_{c}$ or speed $= \sqrt{\frac{2}{3} v^{2} + \frac{2}{3} v^{2}} = \frac{2 \sqrt{2}}{3} v$

Initial kinetic energy

$K_{i} = \frac{1}{2} (m) (2 v)^{2} + \frac{1}{2} (2 m) (v)^{2} = 3 m v^{2}$

Final kinetic energy

$K_{f} = \frac{1}{2} (3 m) \frac{2 \sqrt{2}}{3} v^{2} = \frac{4}{3} m v^{2}$

Fractional loss $= \frac{K_{i} - K_{f}}{K_{i}} \times 100$

$= \frac{(3 m v^{2}) - \frac{4}{3} m v^{2}}{(3 m v^{2})} \times 100 = 56$

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Centre of Mass 3 Question 10

13. A particle of mass $m$ moving in the $x$ -direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ -direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

Answer:

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Centre of Mass 3 Question 10

13. A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

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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13. A particle of mass $m$ moving in the $x$ -direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ -direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to