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A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3?
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A cylinder has a radius R and length L.If the moment of inertia of the...
Explanation:
Moment of Inertia: The moment of inertia of an object is a measure of its resistance to rotational motion around a particular axis.
Equation for Moment of Inertia: The moment of inertia of a cylinder about an axis passing through its centre and normal to its circular face is given by the equation:
I1 = 1/2 mr^2
where m is the mass of the cylinder, and r is the radius of the cylinder.
The moment of inertia of a cylinder about an axis passing through its centre and normal to its length is given by the equation:
I2 = 1/12 mL^2 + 1/4 mr^2
where m is the mass of the cylinder, and L is the length of the cylinder.
Given: The moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length.
Therefore, we can equate the two equations for moment of inertia:
1/2 mr^2 = 1/12 mL^2 + 1/4 mr^2
Multiplying both sides by 12, we get:
6mr^2 = mL^2 + 3mr^2
Simplifying, we get:
3mr^2 = mL^2
Therefore, we can conclude that:
L = √(3)r
Hence, the correct option is (B) L = √3R.
Moment of Inertia: The moment of inertia of an object is a measure of its resistance to rotational motion around a particular axis.
Equation for Moment of Inertia: The moment of inertia of a cylinder about an axis passing through its centre and normal to its circular face is given by the equation:
I1 = 1/2 mr^2
where m is the mass of the cylinder, and r is the radius of the cylinder.
The moment of inertia of a cylinder about an axis passing through its centre and normal to its length is given by the equation:
I2 = 1/12 mL^2 + 1/4 mr^2
where m is the mass of the cylinder, and L is the length of the cylinder.
Given: The moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length.
Therefore, we can equate the two equations for moment of inertia:
1/2 mr^2 = 1/12 mL^2 + 1/4 mr^2
Multiplying both sides by 12, we get:
6mr^2 = mL^2 + 3mr^2
Simplifying, we get:
3mr^2 = mL^2
Therefore, we can conclude that:
L = √(3)r
Hence, the correct option is (B) L = √3R.
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A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3?
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A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3?.
A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3?.
Solutions for A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? in English & in Hindi are available as part of our courses for JEE.
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A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3?, a detailed solution for A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? has been provided alongside types of A cylinder has a radius R and length L.If the moment of inertia of the cylinder about an axis passing through the centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through the centre and normal to its length. Then (A)L=R. (B)L=√3R. (C)L=0. (D)L=R/√3? theory, EduRev gives you an
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