With reference to the figure of a cube of edge \(a\) and mass \(m,\) the following statements are given. (\(O\) is the centre of the cube).

    

Choose the correct statements:
(a) The moment of inertia of the cube about the \(z\)-axis is \(I_z=I_x+I_y\)
(b)  The moment of inertia of the cube about the \(z'\)-axis is \({I_z}'=I_z+\frac{{ma}^2}{2}\)
(c) The moment of inertia of the cube about \(z''\)-axis is = \(=I_z+\frac{{ma}^2}{2}\)
(d) \(I_x=I_y\)
Choose the correct option from the given options:
1. (a, c) 2. (a, d)
3. (b, d) 4. (b, c)
 

Subtopic:  Moment of Inertia |
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Given below are two statements: 
Assertion (A): If the same mass is drawn into the making of a solid sphere and a hollow sphere, the moment of inertia about the diameter of a hollow body is greater than that of a solid body.
Reason (R): The moment of inertia depends on the mass distribution from the axis of rotation and in a hollow sphere, more of the mass is further away from the axis of rotation.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.
Subtopic:  Moment of Inertia |
 86%
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Given below are two statements: 
Assertion (A): When a body rotates in a circle around any axis, all its particles move along a circle in different radii but with the same angular velocity.
Reason (R): The moment of inertia is a vector quantity.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.
Subtopic:  Moment of Inertia |
 65%
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