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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?
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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.
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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
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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?
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