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A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N?
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A solid cylinder of mass 50kg and radius 0.5m is free to rotate about ...
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A solid cylinder of mass 50kg and radius 0.5m is free to rotate about ...
Given:
- Mass of the cylinder (m) = 50 kg
- Radius of the cylinder (r) = 0.5 m
- Angular acceleration (α) = 2 rev/s²
To find:
Tension in the string required to produce the given angular acceleration.
Formula:
The torque (τ) produced by a force (F) acting at a distance (r) from the axis of rotation is given by the equation:
τ = F × r
The torque produced by the tension in the string is equal to the moment of inertia (I) of the cylinder multiplied by the angular acceleration (α):
τ = I × α
The moment of inertia of a solid cylinder about its central axis is given by the equation:
I = (1/2) × m × r²
Calculation:
1. Moment of inertia (I) of the cylinder:
I = (1/2) × m × r²
= (1/2) × 50 kg × (0.5 m)²
= 6.25 kg·m²
2. Torque produced by the tension in the string:
τ = I × α
= 6.25 kg·m² × 2 rev/s²
= 12.5 kg·m²/s²
3. Torque produced by the tension in the string is equal to the torque produced by the force (F) applied at the radius (r):
τ = F × r
4. Solving for the tension in the string (F):
F = τ / r
= 12.5 kg·m²/s² / 0.5 m
= 25 N
Answer:
The tension in the string required to produce an angular acceleration of 2 rev/s² is 25 N. Therefore, the correct option is A. 25N.
- Mass of the cylinder (m) = 50 kg
- Radius of the cylinder (r) = 0.5 m
- Angular acceleration (α) = 2 rev/s²
To find:
Tension in the string required to produce the given angular acceleration.
Formula:
The torque (τ) produced by a force (F) acting at a distance (r) from the axis of rotation is given by the equation:
τ = F × r
The torque produced by the tension in the string is equal to the moment of inertia (I) of the cylinder multiplied by the angular acceleration (α):
τ = I × α
The moment of inertia of a solid cylinder about its central axis is given by the equation:
I = (1/2) × m × r²
Calculation:
1. Moment of inertia (I) of the cylinder:
I = (1/2) × m × r²
= (1/2) × 50 kg × (0.5 m)²
= 6.25 kg·m²
2. Torque produced by the tension in the string:
τ = I × α
= 6.25 kg·m² × 2 rev/s²
= 12.5 kg·m²/s²
3. Torque produced by the tension in the string is equal to the torque produced by the force (F) applied at the radius (r):
τ = F × r
4. Solving for the tension in the string (F):
F = τ / r
= 12.5 kg·m²/s² / 0.5 m
= 25 N
Answer:
The tension in the string required to produce an angular acceleration of 2 rev/s² is 25 N. Therefore, the correct option is A. 25N.
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A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N?
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A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N? 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 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N?.
A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N? 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 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N?.
Solutions for A solid cylinder of mass 50kg and radius 0.5m 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 2rev/s2 is A. 25N B. 50N C. 78.5N D. 157N? in English & in Hindi are available as part of our courses for NEET.
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