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Rotational Motion

269513 Moment of inertia of a thin circular plate of mass $M$ , radius $R$ about an axis passing through its diameter is $I$ . The moment of inertia of a circular ring of mass $M$ , radius $R$ about an axis perpendicular to its plane and passing through its centre is

1

2 I

2

\frac{I}{2}

3

4 I

4

\frac{I}{4}

Explanation:

$I = \frac{M R^{2}}{4}; I^{'} = M R^{2}$

Rotational Motion

269514 The mass of a thin circular plate is $M$ and its radius is $R$ . About an axis in the plane of plate at a perpendicular distance $R / 2$ from centre of plate, its moment of inertia is

1

\frac{{MR}^{2}}{4}

2

\frac{{MR}^{2}}{2}

3

\frac{3 {MR}^{2}}{4}

4

\frac{3 {MR}^{2}}{2}

Explanation:

$I = I_{c} + M d^{2} = \frac{M R^{2}}{4} + M ◻^{2} θ^{2}$

Rotational Motion

269515 In a rectangle $A B C D (B C = 2 A B)$ . The moment of inertia is maximum along axis through

1

BC

2

A B

3

HF

4 EG

Explanation:

perpendicular distance is maximum when the axis of rotation passes through $AB$ , hence M.I about $AB$ is maximum.

Rotational Motion

269516 $M$ is mass and $R$ is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance $\frac{2 R}{3}$ from centre of ring is

1

\frac{2 M R^{2}}{3}

2

\frac{4 M R^{2}}{9}

3

\frac{3 M R^{2}}{8}

4

\frac{17 M R^{2}}{18}

Explanation:

$I = I_{c} + M d^{2}; I_{C} = M R^{2}$ and $d = \frac{2 R}{3}$

Rotational Motion

269513 Moment of inertia of a thin circular plate of mass $M$ , radius $R$ about an axis passing through its diameter is $I$ . The moment of inertia of a circular ring of mass $M$ , radius $R$ about an axis perpendicular to its plane and passing through its centre is

1

2 I

2

\frac{I}{2}

3

4 I

4

\frac{I}{4}

Explanation:

$I = \frac{M R^{2}}{4}; I^{'} = M R^{2}$

Rotational Motion

269514 The mass of a thin circular plate is $M$ and its radius is $R$ . About an axis in the plane of plate at a perpendicular distance $R / 2$ from centre of plate, its moment of inertia is

1

\frac{{MR}^{2}}{4}

2

\frac{{MR}^{2}}{2}

3

\frac{3 {MR}^{2}}{4}

4

\frac{3 {MR}^{2}}{2}

Explanation:

$I = I_{c} + M d^{2} = \frac{M R^{2}}{4} + M ◻^{2} θ^{2}$

Rotational Motion

269515 In a rectangle $A B C D (B C = 2 A B)$ . The moment of inertia is maximum along axis through

1

BC

2

A B

3

HF

4 EG

Explanation:

perpendicular distance is maximum when the axis of rotation passes through $AB$ , hence M.I about $AB$ is maximum.

Rotational Motion

269516 $M$ is mass and $R$ is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance $\frac{2 R}{3}$ from centre of ring is

1

\frac{2 M R^{2}}{3}

2

\frac{4 M R^{2}}{9}

3

\frac{3 M R^{2}}{8}

4

\frac{17 M R^{2}}{18}

Explanation:

$I = I_{c} + M d^{2}; I_{C} = M R^{2}$ and $d = \frac{2 R}{3}$

Rotational Motion

269513 Moment of inertia of a thin circular plate of mass $M$ , radius $R$ about an axis passing through its diameter is $I$ . The moment of inertia of a circular ring of mass $M$ , radius $R$ about an axis perpendicular to its plane and passing through its centre is

1

2 I

2

\frac{I}{2}

3

4 I

4

\frac{I}{4}

Explanation:

$I = \frac{M R^{2}}{4}; I^{'} = M R^{2}$

Rotational Motion

269514 The mass of a thin circular plate is $M$ and its radius is $R$ . About an axis in the plane of plate at a perpendicular distance $R / 2$ from centre of plate, its moment of inertia is

1

\frac{{MR}^{2}}{4}

2

\frac{{MR}^{2}}{2}

3

\frac{3 {MR}^{2}}{4}

4

\frac{3 {MR}^{2}}{2}

Explanation:

$I = I_{c} + M d^{2} = \frac{M R^{2}}{4} + M ◻^{2} θ^{2}$

Rotational Motion

269515 In a rectangle $A B C D (B C = 2 A B)$ . The moment of inertia is maximum along axis through

1

BC

2

A B

3

HF

4 EG

Explanation:

perpendicular distance is maximum when the axis of rotation passes through $AB$ , hence M.I about $AB$ is maximum.

Rotational Motion

269516 $M$ is mass and $R$ is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance $\frac{2 R}{3}$ from centre of ring is

1

\frac{2 M R^{2}}{3}

2

\frac{4 M R^{2}}{9}

3

\frac{3 M R^{2}}{8}

4

\frac{17 M R^{2}}{18}

Explanation:

$I = I_{c} + M d^{2}; I_{C} = M R^{2}$ and $d = \frac{2 R}{3}$

Rotational Motion

269513 Moment of inertia of a thin circular plate of mass $M$ , radius $R$ about an axis passing through its diameter is $I$ . The moment of inertia of a circular ring of mass $M$ , radius $R$ about an axis perpendicular to its plane and passing through its centre is

1

2 I

2

\frac{I}{2}

3

4 I

4

\frac{I}{4}

Explanation:

$I = \frac{M R^{2}}{4}; I^{'} = M R^{2}$

Rotational Motion

269514 The mass of a thin circular plate is $M$ and its radius is $R$ . About an axis in the plane of plate at a perpendicular distance $R / 2$ from centre of plate, its moment of inertia is

1

\frac{{MR}^{2}}{4}

2

\frac{{MR}^{2}}{2}

3

\frac{3 {MR}^{2}}{4}

4

\frac{3 {MR}^{2}}{2}

Explanation:

$I = I_{c} + M d^{2} = \frac{M R^{2}}{4} + M ◻^{2} θ^{2}$

Rotational Motion

269515 In a rectangle $A B C D (B C = 2 A B)$ . The moment of inertia is maximum along axis through

1

BC

2

A B

3

HF

4 EG

Explanation:

perpendicular distance is maximum when the axis of rotation passes through $AB$ , hence M.I about $AB$ is maximum.

Rotational Motion

269516 $M$ is mass and $R$ is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance $\frac{2 R}{3}$ from centre of ring is

1

\frac{2 M R^{2}}{3}

2

\frac{4 M R^{2}}{9}

3

\frac{3 M R^{2}}{8}

4

\frac{17 M R^{2}}{18}

Explanation:

$I = I_{c} + M d^{2}; I_{C} = M R^{2}$ and $d = \frac{2 R}{3}$