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A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?
Image details:- the cylinder is pulled by acting tangentially on the top?
Image details:- the cylinder is pulled by acting tangentially on the top?
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A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of ...
Problem: Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude.
Given:
Mass of cylinder, m
Angle of incline, θ = 37°
To find:
Minimum coefficient of friction, μ
Solution:
Let N be the normal reaction acting on the cylinder and f be the force applied tangentially to keep the cylinder in equilibrium. Force acting downwards, mg = m × g, where g is the acceleration due to gravity.
Resolving forces along the incline:
N × cosθ = mg
N = mg / cosθ
Resolving forces perpendicular to the incline:
f = N × sinθ
Substituting the value of N:
f = mg × sinθ / cosθ
The force of friction acting on the cylinder, Ffriction = μN. To find the minimum coefficient of friction, we need to find the minimum force of friction that can keep the cylinder in equilibrium.
The minimum force of friction can be achieved when the force applied tangentially to the cylinder is minimum. Therefore, the minimum force of friction required to keep the cylinder in equilibrium is the force of gravity acting along the incline, mg × sinθ.
Therefore, μN = mg × sinθ
μ × mg / cosθ = mg × sinθ
μ = sinθ / cosθ
μ = tanθ
Substituting the value of θ:
μ = tan37°
μ = 0.75
Therefore, the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude is 0.75 or 3/4.
Answer: (A) 3/4
Given:
Mass of cylinder, m
Angle of incline, θ = 37°
To find:
Minimum coefficient of friction, μ
Solution:
Let N be the normal reaction acting on the cylinder and f be the force applied tangentially to keep the cylinder in equilibrium. Force acting downwards, mg = m × g, where g is the acceleration due to gravity.
Resolving forces along the incline:
N × cosθ = mg
N = mg / cosθ
Resolving forces perpendicular to the incline:
f = N × sinθ
Substituting the value of N:
f = mg × sinθ / cosθ
The force of friction acting on the cylinder, Ffriction = μN. To find the minimum coefficient of friction, we need to find the minimum force of friction that can keep the cylinder in equilibrium.
The minimum force of friction can be achieved when the force applied tangentially to the cylinder is minimum. Therefore, the minimum force of friction required to keep the cylinder in equilibrium is the force of gravity acting along the incline, mg × sinθ.
Therefore, μN = mg × sinθ
μ × mg / cosθ = mg × sinθ
μ = sinθ / cosθ
μ = tanθ
Substituting the value of θ:
μ = tan37°
μ = 0.75
Therefore, the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude is 0.75 or 3/4.
Answer: (A) 3/4
Community Answer
A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of ...

Balance Torque about point of contact.
F(2r)= mgsin(theta) x r
F= mgsintheta / 2 -- (1)
Balance force
F min + f max = mg sin theta --(2)
f max = mu ( Mg costheta) --(3)
solve 1 ,2 and 3.
We will get
mu= tan ( theta)/ 2 = 3/8
Balance Torque about point of contact.
F(2r)= mgsin(theta) x r
F= mgsintheta / 2 -- (1)
Balance force
F min + f max = mg sin theta --(2)
f max = mu ( Mg costheta) --(3)
solve 1 ,2 and 3.
We will get
mu= tan ( theta)/ 2 = 3/8
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A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top?
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A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top?.
A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass ‘m’ is kept stationary on a fixed incline of 37deg, by applying a force tangentially as shown in the figure. Calculate the minimum coefficient of friction that the surface must have in order to achieve equilibrium of the cylinder by applying a force of minimum magnitude. (A) 3 /4 (B) 3 /8 (C) 3 /16 (D) none of these?Image details:- the cylinder is pulled by acting tangentially on the top?.
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