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Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P?
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Two particles P and Q of masses 3 kg and 6 kg respectively are attache...
**Solution:**
**a) Time taken by Particle Q to fall to the ground:**
Let's assume that the positive direction is upwards. In this case, the acceleration due to gravity acting on Particle Q is -9.8 m/s^2.
Using the second equation of motion, we can find the time taken by Particle Q to fall to the ground.
The initial velocity of Particle Q, u = 0 (as it is released from rest)
The final displacement of Particle Q, s = 15 m
The acceleration of Particle Q, a = -9.8 m/s^2
Using the equation s = ut + (1/2)at^2, we can solve for time (t).
15 = 0*t + (1/2)*(-9.8)*t^2
15 = -4.9t^2
t^2 = -15/-4.9
t^2 = 3.06
t = sqrt(3.06)
t ≈ 1.75 seconds
Therefore, Particle Q takes approximately 1.75 seconds to fall to the ground.
**b) Maximum height ascended by Particle P after Q hits the ground:**
Since the string is inextensible, the distance traveled by Particle Q is equal to the distance traveled by Particle P.
Let's assume that the maximum height ascended by Particle P is h.
The distance traveled by Particle P, s = 15 m
The acceleration due to gravity acting on Particle P, a = 9.8 m/s^2
Using the third equation of motion, we can find the maximum height (h) ascended by Particle P.
s = ut + (1/2)at^2
h = 0*t + (1/2)*9.8*t^2
h = 4.9t^2
Substituting the value of t (1.75 seconds) that we found in part a, we can calculate the maximum height (h).
h = 4.9*(1.75)^2
h ≈ 15.21 m
Therefore, Particle P ascends to a maximum height of approximately 15.21 meters after Particle Q hits the ground.
**c) Time at which Particle Q begins to move again due to motion of P:**
Since Particle P does not reach the pulley, it means that the string does not unwind completely. Therefore, the time at which Particle Q begins to move again due to the motion of P can be calculated by finding the time taken by Particle P to reach the maximum height.
Using the third equation of motion, we can find the time taken by Particle P to reach the maximum height (h) that we found in part b.
h = ut + (1/2)at^2
15 = 0*t + (1/2)*(-9.8)*t^2
15 = -4.9t^2
t^2 = -15/-4.9
t^2 = 3.06
t = sqrt(3.06)
t ≈ 1.75 seconds
Therefore, Particle Q begins to move again due to the motion of P approximately 1.75 seconds after hitting the ground.
**a) Time taken by Particle Q to fall to the ground:**
Let's assume that the positive direction is upwards. In this case, the acceleration due to gravity acting on Particle Q is -9.8 m/s^2.
Using the second equation of motion, we can find the time taken by Particle Q to fall to the ground.
The initial velocity of Particle Q, u = 0 (as it is released from rest)
The final displacement of Particle Q, s = 15 m
The acceleration of Particle Q, a = -9.8 m/s^2
Using the equation s = ut + (1/2)at^2, we can solve for time (t).
15 = 0*t + (1/2)*(-9.8)*t^2
15 = -4.9t^2
t^2 = -15/-4.9
t^2 = 3.06
t = sqrt(3.06)
t ≈ 1.75 seconds
Therefore, Particle Q takes approximately 1.75 seconds to fall to the ground.
**b) Maximum height ascended by Particle P after Q hits the ground:**
Since the string is inextensible, the distance traveled by Particle Q is equal to the distance traveled by Particle P.
Let's assume that the maximum height ascended by Particle P is h.
The distance traveled by Particle P, s = 15 m
The acceleration due to gravity acting on Particle P, a = 9.8 m/s^2
Using the third equation of motion, we can find the maximum height (h) ascended by Particle P.
s = ut + (1/2)at^2
h = 0*t + (1/2)*9.8*t^2
h = 4.9t^2
Substituting the value of t (1.75 seconds) that we found in part a, we can calculate the maximum height (h).
h = 4.9*(1.75)^2
h ≈ 15.21 m
Therefore, Particle P ascends to a maximum height of approximately 15.21 meters after Particle Q hits the ground.
**c) Time at which Particle Q begins to move again due to motion of P:**
Since Particle P does not reach the pulley, it means that the string does not unwind completely. Therefore, the time at which Particle Q begins to move again due to the motion of P can be calculated by finding the time taken by Particle P to reach the maximum height.
Using the third equation of motion, we can find the time taken by Particle P to reach the maximum height (h) that we found in part b.
h = ut + (1/2)at^2
15 = 0*t + (1/2)*(-9.8)*t^2
15 = -4.9t^2
t^2 = -15/-4.9
t^2 = 3.06
t = sqrt(3.06)
t ≈ 1.75 seconds
Therefore, Particle Q begins to move again due to the motion of P approximately 1.75 seconds after hitting the ground.
Community Answer
Two particles P and Q of masses 3 kg and 6 kg respectively are attache...
Can u solve this problems using newtons law
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Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P?
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Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P?.
Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P?.
Solutions for Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? in English & in Hindi are available as part of our courses for JEE.
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Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P?, a detailed solution for Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? has been provided alongside types of Two particles P and Q of masses 3 kg and 6 kg respectively are attached to the ends of a light inextensible string passing over a fixed smooth pulley. when both particles are 15m above the horizontal ground, the system is released from rest. a) find the time taken by Particle Q to fall to the ground. B) Assuming that the particle P does not reach the pulley, find the maximum height ascended by P after Q hit the ground. C)Assuming complete stop of particle Q after it hits the ground, calculate the time which the particle Q begins to move again due to motion of P? theory, EduRev gives you an
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