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Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.?
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Understanding the Pendulum System
When two simple pendulums of equal lengths and masses collide elastically, several important principles of physics come into play.
Key Factors in the System:
- Identical Lengths and Masses: Both pendulums have the same length and mass, which ensures symmetric behavior in their motion.
- Small Angle Approximation: The small angles (q1 and q2) allow us to approximate sin(q) as q, simplifying the equations of motion.
Behavior Before Collision:
- Conservation of Energy: As the pendulums are released, they convert potential energy into kinetic energy. The speed at the lowest point depends only on the height from which they are released.
- Timing of Collisions: If released simultaneously, the pendulums will swing toward each other. The timing of their collisions will depend on their respective angles and the length of the string.
Collision Dynamics:
- Elastic Collision: In an elastic collision, both momentum and kinetic energy are conserved. Given that both pendulums have equal mass, the velocities can be exchanged during the collision.
- Post-Collision Behavior: After the collision, the pendulum that was initially displaced more (greater angle) will transfer some of its momentum to the other, which may now swing up to a higher angle.
Final Observations:
- Resulting Motion: Post-collision, the pendulums will continue to swing in their respective arcs, with energy exchanged between them.
- Periodic Motion: The system can be seen as a coupled oscillator system, leading to interesting patterns of motion.
In summary, the behavior of the pendulums under small angle displacements and elastic collisions can be analyzed using conservation laws, resulting in a dynamic interplay of energy and momentum.
When two simple pendulums of equal lengths and masses collide elastically, several important principles of physics come into play.
Key Factors in the System:
- Identical Lengths and Masses: Both pendulums have the same length and mass, which ensures symmetric behavior in their motion.
- Small Angle Approximation: The small angles (q1 and q2) allow us to approximate sin(q) as q, simplifying the equations of motion.
Behavior Before Collision:
- Conservation of Energy: As the pendulums are released, they convert potential energy into kinetic energy. The speed at the lowest point depends only on the height from which they are released.
- Timing of Collisions: If released simultaneously, the pendulums will swing toward each other. The timing of their collisions will depend on their respective angles and the length of the string.
Collision Dynamics:
- Elastic Collision: In an elastic collision, both momentum and kinetic energy are conserved. Given that both pendulums have equal mass, the velocities can be exchanged during the collision.
- Post-Collision Behavior: After the collision, the pendulum that was initially displaced more (greater angle) will transfer some of its momentum to the other, which may now swing up to a higher angle.
Final Observations:
- Resulting Motion: Post-collision, the pendulums will continue to swing in their respective arcs, with energy exchanged between them.
- Periodic Motion: The system can be seen as a coupled oscillator system, leading to interesting patterns of motion.
In summary, the behavior of the pendulums under small angle displacements and elastic collisions can be analyzed using conservation laws, resulting in a dynamic interplay of energy and momentum.
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Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.?
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Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.?.
Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.?.
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Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.?, a detailed solution for Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? has been provided alongside types of Two simple pendulums of equal lengths and equal bob masses are hung from same point. When strings of pendulums are displaced from vertical positions, by angles q1 and q2 and released, they make elastic collisions with each other in subsequent motion. Neglecting sizes of bobs of pendulums and assuming q1 and q2 are small enough to hold approximation sinq = q, mark the CORRECT alternative.? theory, EduRev gives you an
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