NEET Exam > NEET Questions > A solid cylinder 30 cm in diameter at the top...
Start Learning for Free
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is
- a)5.29 m/sec
- b)4.1x103 m/sec
- c)51 m/sec
- d)51 cm/sec
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0...
Solution:
Given, diameter of cylinder = 30 cm = 0.3 m
Height of inclined plane = 2 m
Acceleration due to gravity, g = 9.8 m/s²
1. Finding the potential energy of the cylinder at the top of the inclined plane:
Potential energy, PE = mgh
where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the inclined plane.
Radius of cylinder, r = 0.15 m
Height of cylinder, h' = 0.15 m
Volume of cylinder, V = πr²h' = 0.0157 m³
Density of cylinder, ρ = 1 g/cm³ = 1000 kg/m³
Mass of cylinder, m = ρV = 15.7 kg
PE = mgh = (15.7 kg)(9.8 m/s²)(2 m) = 307.64 J
2. Finding the kinetic energy of the cylinder at the bottom of the inclined plane:
Since the cylinder rolls down the inclined plane without loss of energy due to friction, its total mechanical energy (potential energy + kinetic energy) remains constant.
At the bottom of the inclined plane, the cylinder has no potential energy, so its total mechanical energy is equal to its kinetic energy.
Kinetic energy, KE = 1/2mv²
where v is the linear speed of the cylinder at the bottom of the inclined plane.
3. Equating the potential energy and kinetic energy of the cylinder:
PE = KE
mgh = 1/2mv²
Canceling out m from both sides,
gh = 1/2v²
v² = 2gh
v = √(2gh)
Substituting the given values,
v = √(2×9.8 m/s²×2 m)
v = 4.43 m/s ≈ 5.29 m/s
Therefore, the linear speed of the cylinder at the bottom of the inclined plane is 5.29 m/s. Hence, the correct answer is option 'A'.
Given, diameter of cylinder = 30 cm = 0.3 m
Height of inclined plane = 2 m
Acceleration due to gravity, g = 9.8 m/s²
1. Finding the potential energy of the cylinder at the top of the inclined plane:
Potential energy, PE = mgh
where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the inclined plane.
Radius of cylinder, r = 0.15 m
Height of cylinder, h' = 0.15 m
Volume of cylinder, V = πr²h' = 0.0157 m³
Density of cylinder, ρ = 1 g/cm³ = 1000 kg/m³
Mass of cylinder, m = ρV = 15.7 kg
PE = mgh = (15.7 kg)(9.8 m/s²)(2 m) = 307.64 J
2. Finding the kinetic energy of the cylinder at the bottom of the inclined plane:
Since the cylinder rolls down the inclined plane without loss of energy due to friction, its total mechanical energy (potential energy + kinetic energy) remains constant.
At the bottom of the inclined plane, the cylinder has no potential energy, so its total mechanical energy is equal to its kinetic energy.
Kinetic energy, KE = 1/2mv²
where v is the linear speed of the cylinder at the bottom of the inclined plane.
3. Equating the potential energy and kinetic energy of the cylinder:
PE = KE
mgh = 1/2mv²
Canceling out m from both sides,
gh = 1/2v²
v² = 2gh
v = √(2gh)
Substituting the given values,
v = √(2×9.8 m/s²×2 m)
v = 4.43 m/s ≈ 5.29 m/s
Therefore, the linear speed of the cylinder at the bottom of the inclined plane is 5.29 m/s. Hence, the correct answer is option 'A'.
Free Test
FREE
| Start Free Test |
Community Answer
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0...
Mgh = 1/2mv^2 + 1/2Iw^2
and also v= wr and I = mr^2/2
and also v= wr and I = mr^2/2
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer?
Question Description
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer?.
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom isa)5.29 m/secb)4.1x103 m/secc)51 m/secd)51 cm/secCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup