SATHEE: Simple Harmonic Motion 5 Question 15

Simple Harmonic Motion 5 Question 15

20. A block with mass $M$ is connected by a massless spring with stiffness constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_{0}$ . Consider two cases : (i) when the block is at $x_{0}$ and (ii) when the block is at $x = x_{0} + A$ . In both the cases, a particle with mass $m (< M)$ is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass $m$ is placed on the mass $M$ ?

(2016 Adv.)

(a) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m + M}}$ , whereas in the second case it remains unchanged

(b) The final time period of oscillation in both the cases is same

(d) The instantaneous speed at $x_{0}$ of the combined masses decreases in both the cases

Show Answer

Answer:

Correct Answer: 20. (a, b, d) 21. (b, d) 22. (a, d)

Solution:

Case-1

Case-2

In case-1,

$\begin{aligned} M v_{1} & = (M + m) v_{2} \\ v_{2} & = \frac{M}{M + m} v_{1} \\ \sqrt{\frac{k}{M + m}} A_{2} & = \frac{M}{M + m} \sqrt{\frac{k}{M}} A_{1} \\ A_{2} & = \sqrt{\frac{k}{M + m}} A_{1} \end{aligned}$

In case-2 $A_{2} - A_{1}$

$T = 2 π \sqrt{\frac{M + m}{k}} in both cases.$

Total energy decreases in first case whereas remain same in $2^{nd}$ case. Instantaneous speed at $x_{0}$ decreases in both cases.

पिछला

अगला

Simple Harmonic Motion 5 Question 15

Answer:

Case-2

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 5 Question 15

Answer:

Case-2

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu