SATHEE: Work Energy And Power Question 278

Work Energy And Power Question 278

Question: Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be

Options:

A) $\frac{u}{12} (\hat{i} + \sqrt{3} \hat{j})$

B) $\frac{u}{12} (\hat{i} - \sqrt{3} \hat{j})$

C) $\frac{u}{12} (- \hat{i} + \sqrt{3} \hat{j})$

D) $\frac{u}{12} (- \hat{i} - \sqrt{3} \hat{j})$

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Answer:

Correct Answer: D

Solution:

[d] From the law of conservation of momentum we know that,

$m_{1} u_{1} + m_{2} u_{2} + \dots = m_{1} v_{1} + m_{2} v_{2} + \dots$ Given $m_{1} = m, m_{2} = 2 m a n d m_{3} = 3 m$

and $u_{1} = 3 u, u_{2} = 2 u a n d u_{3} = u$

Let the velocity when they stick $= \vec{v}$

Then, according to question, $m \times 3 u (\hat{i}) + 2 m \times 2 u (- \hat{i} c o s 60^{\circ} - \hat{j} \sin 60^{\circ})$

$+ 3 m \times u (- \hat{i} c o s 60^{\circ} + \hat{j} s i n 60^{\circ}) = (m + 2 m + 3 m) \vec{v}$

$\Rightarrow 3 m u \hat{i} - 4 m u \frac{\hat{i}}{2} 4 m u (\frac{\sqrt{3}}{2} \hat{j}) - 3 m u \frac{\hat{i}}{2}$

$+ 3 m u (\frac{\sqrt{3}}{2} \hat{j}) = 6 m \vec{v}$

$\Rightarrow m u \hat{i} - \frac{3}{2} m u \hat{i} - \frac{\sqrt{3}}{2} m u \hat{j} = 6 m \vec{v}$

$\Rightarrow - \frac{1}{2} m u \hat{i} - \frac{\sqrt{3}}{2} m u \hat{j} = 6 m \vec{v}$

$\Rightarrow \vec{v} = \frac{u}{12} (- \hat{i} - \sqrt{3} \hat{j})$

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अगला

Work Energy And Power Question 278

Question: Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be

Options:

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Work Energy And Power Question 278

Question: Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be

Options:

Answer:

Solution:

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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