JEE Exam > JEE Questions > A pendulum consists of a bob of mass m = 0.1 ...
Start Learning for Free
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 K is ______.
Correct answer is '0.16'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A pendulum consists of a bob of mass m = 0.1 kg and a massless inexten...
Given data:
- Mass of the bob, m = 0.1 kg
- Length of the string, L = 1.0 m
- Height of suspension point above the floor, H = 0.9 m
- Horizontal impulse imparted to the bob, P = 0.2 kg-m/s
- Magnitude of angular momentum just before lift-off, J = ?
- Kinetic energy just after lift-off, K = ?
Finding the angular momentum just before lift-off:
- The angular momentum of an object is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.
- The moment of inertia of a pendulum bob of mass m and length L suspended from a point at a distance H from the floor is I = m(L^2 + H^2).
- Initially, the bob is at rest and its angular velocity is zero, so its angular momentum is also zero.
- The impulse P causes the bob to slide horizontally, but since there is no friction, there is no torque acting on the system, and the angular momentum remains zero.
- When the string becomes taut and the bob lifts off the floor, the system starts rotating about the point of suspension.
- At this instant, the angular momentum of the system is given by J = Iω, where ω is the angular velocity of the bob just before lift-off.
- Substituting the values of m, L, and H, we get I = 0.19 kg-m^2.
- To find ω, we can use conservation of energy. Initially, the bob has only potential energy, which is converted to kinetic energy just before lift-off. At lift-off, all the potential energy is converted to kinetic energy, so we can equate the two expressions:
mgh = (1/2)mv^2
where g is the acceleration due to gravity, h is the initial height of the bob above the floor (which is zero), and v is the velocity of the bob just before lift-off.
Substituting the given values, we get v = sqrt(2gh) = sqrt(2*9.81*0.9) = 3.0 m/s.
The angular velocity ω is given by ω = v/L = 3.0 rad/s.
Substituting this value in the expression for angular momentum, we get J = 0.57 kg-m^2/s.
Finding the kinetic energy just after lift-off:
- The kinetic energy of a rotating object is given by K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
- At lift-off, the system has only kinetic energy, and no potential energy, since the bob is at the same height as the point of suspension.
- Substituting the values of I and ω, we get K = (1/2)(0.19)(3.0)^2 = 0.855 J.
- However, this is the total kinetic energy of the system, which includes the kinetic energy of the bob and the string. We are interested only in the kinetic energy of the bob.
- The kinetic energy of the string can be neglected, since it is massless and has a negligible moment of inertia.
- The kinetic energy of the bob is given by Kbob = (1/2)mbv
- Mass of the bob, m = 0.1 kg
- Length of the string, L = 1.0 m
- Height of suspension point above the floor, H = 0.9 m
- Horizontal impulse imparted to the bob, P = 0.2 kg-m/s
- Magnitude of angular momentum just before lift-off, J = ?
- Kinetic energy just after lift-off, K = ?
Finding the angular momentum just before lift-off:
- The angular momentum of an object is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.
- The moment of inertia of a pendulum bob of mass m and length L suspended from a point at a distance H from the floor is I = m(L^2 + H^2).
- Initially, the bob is at rest and its angular velocity is zero, so its angular momentum is also zero.
- The impulse P causes the bob to slide horizontally, but since there is no friction, there is no torque acting on the system, and the angular momentum remains zero.
- When the string becomes taut and the bob lifts off the floor, the system starts rotating about the point of suspension.
- At this instant, the angular momentum of the system is given by J = Iω, where ω is the angular velocity of the bob just before lift-off.
- Substituting the values of m, L, and H, we get I = 0.19 kg-m^2.
- To find ω, we can use conservation of energy. Initially, the bob has only potential energy, which is converted to kinetic energy just before lift-off. At lift-off, all the potential energy is converted to kinetic energy, so we can equate the two expressions:
mgh = (1/2)mv^2
where g is the acceleration due to gravity, h is the initial height of the bob above the floor (which is zero), and v is the velocity of the bob just before lift-off.
Substituting the given values, we get v = sqrt(2gh) = sqrt(2*9.81*0.9) = 3.0 m/s.
The angular velocity ω is given by ω = v/L = 3.0 rad/s.
Substituting this value in the expression for angular momentum, we get J = 0.57 kg-m^2/s.
Finding the kinetic energy just after lift-off:
- The kinetic energy of a rotating object is given by K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
- At lift-off, the system has only kinetic energy, and no potential energy, since the bob is at the same height as the point of suspension.
- Substituting the values of I and ω, we get K = (1/2)(0.19)(3.0)^2 = 0.855 J.
- However, this is the total kinetic energy of the system, which includes the kinetic energy of the bob and the string. We are interested only in the kinetic energy of the bob.
- The kinetic energy of the string can be neglected, since it is massless and has a negligible moment of inertia.
- The kinetic energy of the bob is given by Kbob = (1/2)mbv
Free Test
FREE
| Start Free Test |
Community Answer
A pendulum consists of a bob of mass m = 0.1 kg and a massless inexten...
As the bob lifts off, due to impulse of string, angular momentum will be conserved about the suspension point.
⇒ Jf = Ji
⇒ Mvfℓ sin 90° = 0.18
⇒ vf = 1.8 m/s
⇒ Kinetic energy after lifting off
⇒ Jf = Ji
⇒ Mvfℓ sin 90° = 0.18
⇒ vf = 1.8 m/s
⇒ Kinetic energy after lifting off
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning 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 K is ______.Correct answer is '0.16'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. 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 K is ______.Correct answer is '0.16'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup