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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2 is :
- a)157 N
- b)78.5 N
- c)25 πN
- d)50 N
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate abou...
Olution per second squared is:
First, we need to find the moment of inertia of the cylinder about its axis of rotation. The moment of inertia of a solid cylinder is given by:
I = (1/2)mr^2
where m is the mass of the cylinder and r is its radius.
Plugging in the values, we get:
I = (1/2)(50 kg)(0.5 m)^2 = 6.25 kg m^2
Next, we can use Newton's second law for rotational motion, which relates the torque applied to an object to its angular acceleration:
τ = Iα
where τ is the torque, α is the angular acceleration, and I is the moment of inertia.
We want to find the tension in the string, which will provide the torque needed to produce the desired angular acceleration. The tension in the string will create a torque equal to the product of the tension force and the radius of the cylinder:
τ = Tr
where T is the tension in the string and r is the radius of the cylinder.
Substituting into the equation for torque, we get:
Tr = Iα
Solving for T, we get:
T = (Iα)/r
Plugging in the values, we get:
T = (6.25 kg m^2)(2 rev/s^2)/(0.5 m) = 50 N
Therefore, the tension in the string required to produce an angular acceleration of 2 revolutions per second squared is 50 N.
First, we need to find the moment of inertia of the cylinder about its axis of rotation. The moment of inertia of a solid cylinder is given by:
I = (1/2)mr^2
where m is the mass of the cylinder and r is its radius.
Plugging in the values, we get:
I = (1/2)(50 kg)(0.5 m)^2 = 6.25 kg m^2
Next, we can use Newton's second law for rotational motion, which relates the torque applied to an object to its angular acceleration:
τ = Iα
where τ is the torque, α is the angular acceleration, and I is the moment of inertia.
We want to find the tension in the string, which will provide the torque needed to produce the desired angular acceleration. The tension in the string will create a torque equal to the product of the tension force and the radius of the cylinder:
τ = Tr
where T is the tension in the string and r is the radius of the cylinder.
Substituting into the equation for torque, we get:
Tr = Iα
Solving for T, we get:
T = (Iα)/r
Plugging in the values, we get:
T = (6.25 kg m^2)(2 rev/s^2)/(0.5 m) = 50 N
Therefore, the tension in the string required to produce an angular acceleration of 2 revolutions per second squared is 50 N.
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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect answer is option 'A'. Can you explain this answer?
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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect 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 of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect 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 of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect answer is option 'A'. Can you explain this answer?.
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect 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 of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect 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 of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2is :a) 157 Nb)78.5 Nc)25 πNd)50 NCorrect answer is option 'A'. Can you explain this answer?.
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