This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Moment of Inertia”.
1. Moment of inertia, of a spinning body about an axis, doesn’t depend on which of the following factors?
a) Distribution of mass around axis
b) Orientation of axis
d) Angular velocity
Explanation: Moment of inertia is the summation of product of mass and perpendicular distance from the axis squared of each particle. More the mass, more will be its value. It depends on perpendicular distance hence, it will depend on orientation and distance of particles from the axis. But, it doesn’t depend on the angular velocity. As the body having a particular value of moment of inertia can achieve any value of angular velocity depending on the torque applied on it.
2. Two cylinders have the same mass and radius. One is hollow and the other is solid. Which one will have the greater moment of inertia about the central axis?
a) Hollow cylinder
b) Solid cylinder
c) Same for both
d) Depends on length of cylinder
Explanation: The hollow one will have greater density as both have the same mass and it has to be distributed uniformly. Thus, the summation of product of mass and perpendicular distance from the axis squared of each particle will be more for the hollow cylinder. And hence, it has more moment of inertia.
3. A solid disc has a mass of 10kg and radius 1m. Find its radius of gyration.
Explanation: Moment of inertia of disc = MR2/2 = 10*1/2 = 5kgm2.
Radius of gyration ‘k’ is given by the expression: I = Mk2
∴ k = √(I/M)
= √(5/10) = 0.707m.
4. What is the moment of inertia of a rod about an axis passing through the centre and perpendicular to its central axis? Given that mass of rod is 1kg, length = 10cm.
Explanation: Let the moment of inertia be I.
And M & I be the mass and length of rod respectively.
For the given condition,
I = MI2/12
= 1*0.01/12 = 0.00083kgm2.
5. The moment of inertia of a solid sphere is 10kgm2. What will be the moment of inertia of a very thin spherical shell of the same mass and radius as that of the solid sphere?
Explanation: Moment of inertia of solid sphere ‘I1’ = 2/5 MR2 = 10kgm2.
Moment of inertia of thin spherical shell ‘I2’= 2/3 MR2.
∴ I2 = 5/3I1
= 5/3 * 10 = 16.67kgm2.
6. What is the ratio of moment of inertia of a ring to a disc? Given that both have masses in the ratio 2:1 & radii in the ratio 1:2 respectively.
Explanation: Moment of inertia of ring = MR2& moment of inertia of disc = MR2/2.
Mass ratio = 2:1, Radii ratio = 1:2.
Thus ratio of moment of inertia = 2MrRr2/MdRd2
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