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Consider a cone which is hollow from the inside. The upper compartment is filled with water which slowly drips down to lower one. Once all the water has come to the lower part, the MOI of the arrangement about the given axis (assuming that there is enough viscosity so that the water rotates with the cone)

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Important Questions on Rotational Motion

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 128

The moment of inertia of a thin uniform rod of mass

M

and length

L

about an axis perpendicular to the rod through its centre is

I

. The moment of inertia of the rod about an axis perpendicular to the rod through its end point is

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 129

Two loops

P

and

Q

are made from a uniform wire. The radii of

P

and

Q

are

r_{1}

and

r_{2}

respectively and their moments of inertia are

I_{1}

and

I_{2}

respectively. If

\frac{I_{2}}{I_{1}} = 4

then,

\frac{r_{2}}{r_{1}}

is equal to

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 130

Three thin uniform rods, each of mass

M

and length

L

, are placed along the three axes of a cartesian coordinate system with one end of each rod at the origin. The moment of inertia of the system about the

z

-axis will be,

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 131

Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is, (Mass of the ring

= m

, radius

= r

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 133

The moment of inertia of a uniform circular disc about its diameter is

200 gm {cm}^{2} .

Then its moment of inertia about an axis passing through its centre and perpendicular to its circular face is

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 134

The moment of inertia of disc about an axis perpendicular to its plane and passing through its centre is

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

. Its moment of inertia about a tangent in its plane

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 135

A hollow cylinder has mass

M

, outside radius

R_{2}

and inside radius

R_{1}

. Its moment of inertia about an axis parallel to its symmetry axis and tangential to the outer surface is equal to

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Physics Crash Course MHT-CET>Chapter 4 - Rotational Motion>Exercise 1>Q 136

Four solid spheres each of mass

M

and radius

R

are placed at four corners of a light square frame of side length

4 R

such that centres of spheres coincide with corners of the square. What will be the moment of inertia of the system about an axis normal to the plane of the frame and passing through its centre?

Important Questions on Rotational Motion

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