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A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.
Q. The value of J is ______.
Correct answer is '0.18'. Can you explain this answer?
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Most Upvoted Answer
A pendulum consists of a bob of mass m = 0.1 kg and a massless inexten...
Analysis:
To find the magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off, we need to consider the conservation of angular momentum.
Solution:
Let's break down the problem step by step:
Step 1: Identifying the given information:
- Mass of the bob, m = 0.1 kg
- Length of the string, L = 1.0 m
- Height of the fixed point above the floor, H = 0.9 m
- Horizontal impulse imparted to the bob, P = 0.2 kg-m/s
Step 2: Finding the initial angular momentum:
The bob is initially at rest, so its initial angular momentum is zero.
Step 3: Finding the final angular momentum:
When the bob lifts off the floor, the string becomes taut and the pendulum starts swinging. At this instant, the angular momentum is given by the equation:
J = Iω
Where J is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Step 4: Calculating the moment of inertia (I):
The moment of inertia for a simple pendulum is given by the equation:
I = mL^2
Substituting the given values:
I = (0.1 kg)(1.0 m)^2 = 0.1 kg-m^2
Step 5: Finding the angular velocity (ω):
To find the angular velocity, we can use the equation for linear velocity:
v = ωr
Where v is the linear velocity, ω is the angular velocity, and r is the radius of the circular path.
In this case, the linear velocity can be calculated by equating the initial and final kinetic energies:
0.5mv^2 = 0.5Iω^2
Substituting the given values:
0.5(0.1 kg)v^2 = 0.5(0.1 kg-m^2)ω^2
Simplifying:
v^2 = ω^2(0.1 m^2)
Step 6: Determining the radius (r):
The radius of the circular path is the length of the string, L.
Therefore, r = L = 1.0 m
Step 7: Substituting values and solving for ω:
Using the equation v = ωr, we can substitute the values to solve for ω:
v^2 = ω^2(0.1 m^2)
v^2 = ω^2(1.0 m)^2
v^2 = ω^2
ω = v
Step 8: Calculating the kinetic energy (K):
The kinetic energy of the pendulum just after lift-off can be calculated using the equation:
K = 0.5Iω^2
Substituting the values:
K = 0.5(0.1 kg-m^2)(v^2)
Step 9: Substituting values and solving for K:
Using the equation v = P/m, we can substitute the values to solve for K:
K = 0.5(
To find the magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off, we need to consider the conservation of angular momentum.
Solution:
Let's break down the problem step by step:
Step 1: Identifying the given information:
- Mass of the bob, m = 0.1 kg
- Length of the string, L = 1.0 m
- Height of the fixed point above the floor, H = 0.9 m
- Horizontal impulse imparted to the bob, P = 0.2 kg-m/s
Step 2: Finding the initial angular momentum:
The bob is initially at rest, so its initial angular momentum is zero.
Step 3: Finding the final angular momentum:
When the bob lifts off the floor, the string becomes taut and the pendulum starts swinging. At this instant, the angular momentum is given by the equation:
J = Iω
Where J is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Step 4: Calculating the moment of inertia (I):
The moment of inertia for a simple pendulum is given by the equation:
I = mL^2
Substituting the given values:
I = (0.1 kg)(1.0 m)^2 = 0.1 kg-m^2
Step 5: Finding the angular velocity (ω):
To find the angular velocity, we can use the equation for linear velocity:
v = ωr
Where v is the linear velocity, ω is the angular velocity, and r is the radius of the circular path.
In this case, the linear velocity can be calculated by equating the initial and final kinetic energies:
0.5mv^2 = 0.5Iω^2
Substituting the given values:
0.5(0.1 kg)v^2 = 0.5(0.1 kg-m^2)ω^2
Simplifying:
v^2 = ω^2(0.1 m^2)
Step 6: Determining the radius (r):
The radius of the circular path is the length of the string, L.
Therefore, r = L = 1.0 m
Step 7: Substituting values and solving for ω:
Using the equation v = ωr, we can substitute the values to solve for ω:
v^2 = ω^2(0.1 m^2)
v^2 = ω^2(1.0 m)^2
v^2 = ω^2
ω = v
Step 8: Calculating the kinetic energy (K):
The kinetic energy of the pendulum just after lift-off can be calculated using the equation:
K = 0.5Iω^2
Substituting the values:
K = 0.5(0.1 kg-m^2)(v^2)
Step 9: Substituting values and solving for K:
Using the equation v = P/m, we can substitute the values to solve for K:
K = 0.5(
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Community Answer
A pendulum consists of a bob of mass m = 0.1 kg and a massless inexten...
Ji = MViHsin90°
= 0.2 0.9 = 0.18 kg-m2/s
= 0.2 0.9 = 0.18 kg-m2/s
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A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer?
Question Description
A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer?.
A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer?.
Solutions for A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer?, a detailed solution for A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? has been provided alongside types of A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K joules.Q. The value of J is ______.Correct answer is '0.18'. Can you explain this answer? tests, examples and also practice JEE tests.
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