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A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.
length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.
length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.
- a)Time period of SHM is
- b)The transitional kinetic energy of the cylinder at equilibrium point is
- c)The rotational kinetic energy of the cylinder at equilibrium point is
- d)Time period of motion is
Correct answer is option 'A,B,C'. Can you explain this answer?
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Verified Answer
A solid cylinder of mass M is attached to horizontal spring of force c...
Let X0 be the equilibrium length of the spring. This is stretched by a length L So. the initial length of the spring xi = (X0 + l).
Potential energy stored in spring
When the spring is released, say att = 0. the cylinder rolls without slipping being pulled by the spring. Consider the situation at time t. Letthe centre of mass be at a distance x from the oiigin O. At this instant.
K .E . (translational) of cylinder = 1/2 mv2
and K.E. (rotational) of cylinder
where v = linear velocity of cylinder
∴ Total energy of cylinder
...(i)
Instantaneous extension of spring = (x - x0)
Potential energy of the spring
∴ Loss of P.E. =
...(ii)
Applying the law of conservation of energy, we have gain in K.E. = loss is potential energy
Differentiating on both sides with respect to t and considering l and x0 constant we get
As x is constant this equation can be written as
This is equation of S.H.M.
∴
At equilibrium position, the potential energy is completely converted to kinetic energy
or
Further,
Potential energy stored in spring
When the spring is released, say att = 0. the cylinder rolls without slipping being pulled by the spring. Consider the situation at time t. Letthe centre of mass be at a distance x from the oiigin O. At this instant.
K .E . (translational) of cylinder = 1/2 mv2
and K.E. (rotational) of cylinder
where v = linear velocity of cylinder
∴ Total energy of cylinder
...(i)Instantaneous extension of spring = (x - x0)
Potential energy of the spring
∴ Loss of P.E. =
...(ii)Applying the law of conservation of energy, we have gain in K.E. = loss is potential energy
Differentiating on both sides with respect to t and considering l and x0 constant we get
As x is constant this equation can be written as
This is equation of S.H.M.
∴
At equilibrium position, the potential energy is completely converted to kinetic energy
or
Further,
Most Upvoted Answer
A solid cylinder of mass M is attached to horizontal spring of force c...
Let X0 be the equilibrium length of the spring. This is stretched by a length L So. the initial length of the spring xi = (X0 + l).
Potential energy stored in spring
When the spring is released, say att = 0. the cylinder rolls without slipping being pulled by the spring. Consider the situation at time t. Letthe centre of mass be at a distance x from the oiigin O. At this instant.
K .E . (translational) of cylinder = 1/2 mv2
and K.E. (rotational) of cylinder
where v = linear velocity of cylinder
∴ Total energy of cylinder
...(i)
Instantaneous extension of spring = (x - x0)
Potential energy of the spring
∴ Loss of P.E. =
...(ii)
Applying the law of conservation of energy, we have gain in K.E. = loss is potential energy
Differentiating on both sides with respect to t and considering l and x0 constant we get
As x is constant this equation can be written as
This is equation of S.H.M.
∴
At equilibrium position, the potential energy is completely converted to kinetic energy
or
Further,
Potential energy stored in spring
When the spring is released, say att = 0. the cylinder rolls without slipping being pulled by the spring. Consider the situation at time t. Letthe centre of mass be at a distance x from the oiigin O. At this instant.
K .E . (translational) of cylinder = 1/2 mv2
and K.E. (rotational) of cylinder
where v = linear velocity of cylinder
∴ Total energy of cylinder
...(i)Instantaneous extension of spring = (x - x0)
Potential energy of the spring
∴ Loss of P.E. =
...(ii)Applying the law of conservation of energy, we have gain in K.E. = loss is potential energy
Differentiating on both sides with respect to t and considering l and x0 constant we get
As x is constant this equation can be written as
This is equation of S.H.M.
∴
At equilibrium position, the potential energy is completely converted to kinetic energy
or
Further,
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A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer?
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A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer?.
A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer?.
Solutions for A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer?, a detailed solution for A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? has been provided alongside types of A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid cylinder of mass M is attached to horizontal spring of force constant k as shown in figure. The spring is first stretched by.length l, by moving cylinder to the left. When the system is released from rest, the cylinder rolls along the horizontal surface without slipping. Centre of mass of the cylinder executes simple harmonic motion.a)Time period of SHM isb)The transitional kinetic energy of the cylinder at equilibrium point isc)The rotational kinetic energy of the cylinder at equilibrium point isd)Time period of motion isCorrect answer is option 'A,B,C'. Can you explain this answer? tests, examples and also practice Physics tests.
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