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Physics Part-I

System of Particles and Rotational Motion

(a) Find the moment of inertia of a sphere about a tangent to

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

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Chapter 3: Motion in Straight Line

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Chapter 5: Laws of motion

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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be

2 M R^{2} /5

, where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be

M R^{2} /4

, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?

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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be $2 M R^{2} /5$ , where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be $M R^{2} /4$ , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Name: Video solution 1: [Solved] (a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR2/5, where M is the mass of the sphere and R is the radius of the sphere. (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge. - Physics Part-I
Uploaded: 2022-04-10T12:24:58.000Z
Duration: 5 min

Views: 5,511 students

Updated on: Sep 25, 2022

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Physics Part-I (NCERT)

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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be

2 M R^{2} /5

, where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be

M R^{2} /4

, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

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Text solutionVerified

(a)

The moment of inertia (M.I.) of a sphere about its diameter

= 2 M R^{2} /5

According to the theorem of parallel axes, the moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

The M.I. about a tangent of the sphere =

2 M R^{2} /5 + M R^{2} = 7 M R^{2} /5

(b)

The moment of inertia of a disc about its diameter =

M R^{2} /4

According to the theorem of perpendicular axis, the moment of inertia of a planar body (laa) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.

The M.I. of the disc about an axis normal to the disc through the center

= M R^{2} /4 + M R^{2} /4 = M R^{2} /2

Now, Applying the theorem of parallel axes:

The moment of inertia about an axis normal to the disc and passing through a point on its edge

= M R^{2} /2 + M R^{2} = 3 M R^{2} /2

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Practice more questions from Physics Part-I (NCERT)

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be

2 M R^{2} /5

, where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be

M R^{2} /4

, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

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Question Text	(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be $2 M R^{2} /5$ , where M is the mass of the sphere and R is the radius of the sphere. (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be $M R^{2} /4$ , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
Updated On	Sep 25, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	297
Avg. Video Duration	13 min

Text solutionVerified

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