Mechanical Engineering Exam > Mechanical Engineering Questions > A hartnell governor having equal arms is acte...
Start Learning for Free
A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm is
- a)50 N/cm
- b)100 N/cm
- c)150 N/cm
- d)None
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A hartnell governor having equal arms is acted upon by centrifugal for...
Solution:
Given,
Centrifugal force at radius r1 = 500 N
Centrifugal force at radius r2 = 250 N
Radius r1 = 10 cm
Radius r2 = 5 cm
Let the stiffness of the spring used in the governor be k N/cm.
The centrifugal force acting on the governor is balanced by the spring force.
Therefore, we can write the equation of equilibrium as:
k(x1 + x2) = F1 + F2
where x1 and x2 are the displacements of the arms from their mean position.
x1 = r1θ, x2 = r2θ (where θ is the angular displacement of the arms)
F1 = m1ω^2r1, F2 = m2ω^2r2
where m1 and m2 are the masses of the arms and ω is the angular velocity of the governor.
Substituting the values of x1, x2, F1, and F2 in the equation of equilibrium, we get:
k(r1 + r2)θ = m1ω^2r1 + m2ω^2r2
k = (m1ω^2r1 + m2ω^2r2)/(r1 + r2)θ
Given, m1 = m2 (equal arms)
k = 2mω^2r/(r1 + r2)θ
Substituting the given values, we get:
k = 2(1 kg)(10 rad/s)^2(10 cm)/(10 cm + 5 cm)
k = 100 N/cm
Therefore, the stiffness of the spring used in the governor is 100 N/cm. Hence, option B is the correct answer.
Given,
Centrifugal force at radius r1 = 500 N
Centrifugal force at radius r2 = 250 N
Radius r1 = 10 cm
Radius r2 = 5 cm
Let the stiffness of the spring used in the governor be k N/cm.
The centrifugal force acting on the governor is balanced by the spring force.
Therefore, we can write the equation of equilibrium as:
k(x1 + x2) = F1 + F2
where x1 and x2 are the displacements of the arms from their mean position.
x1 = r1θ, x2 = r2θ (where θ is the angular displacement of the arms)
F1 = m1ω^2r1, F2 = m2ω^2r2
where m1 and m2 are the masses of the arms and ω is the angular velocity of the governor.
Substituting the values of x1, x2, F1, and F2 in the equation of equilibrium, we get:
k(r1 + r2)θ = m1ω^2r1 + m2ω^2r2
k = (m1ω^2r1 + m2ω^2r2)/(r1 + r2)θ
Given, m1 = m2 (equal arms)
k = 2mω^2r/(r1 + r2)θ
Substituting the given values, we get:
k = 2(1 kg)(10 rad/s)^2(10 cm)/(10 cm + 5 cm)
k = 100 N/cm
Therefore, the stiffness of the spring used in the governor is 100 N/cm. Hence, option B is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
A hartnell governor having equal arms is acted upon by centrifugal for...
K = w/r+w/r
=500/10+250/5
=50+50
=100
=500/10+250/5
=50+50
=100
|
Explore Courses for Mechanical Engineering exam
|
|
Top Courses for Mechanical EngineeringView all
Question Description
A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer?.
A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hartnell governor having equal arms is acted upon by centrifugal force of 500N and 250 N at radius of 10 cm and 5 cm respectively. The stiffness of the spring used in governor in N/cm isa)50 N/cmb)100 N/cmc)150 N/cmd)NoneCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily