The moment of inertia depends on the distribution of mass about the axis of rotation and its SI unit is kg m², so this Class 11 sheet opens with the inertia dependence and its unit. The torque answer Iα and the ring inertia MR² appear in the key.
Key Takeaways
Moment of inertia depends on the distribution of mass about the axis (Q1).
The SI unit of moment of inertia is kg m² (Q2).
Q3 records torque as Iα.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The moment of inertia of a body depends on
(a) Its mass only(b) The distribution of its mass about the axis of rotation(c) Its velocity(d) The force applied
2.The SI unit of moment of inertia is
(a) kg m(b) kg m²(c) kg/m(d) N m
3.The torque τ acting on a body is equal to
(a) Iα(b) ma(c) mv(d) F/v
4.The moment of inertia of a ring of mass M and radius R about its central axis is
(a) MR²/2(b) MR²(c) 2MR²(d) MR²/4
5.The centre of mass of a uniform rod is located at
(a) One end(b) Its midpoint(c) Outside the rod(d) One-quarter from an end
6.The angular momentum L of a body is equal to
(a) Iω(b) Iα(c) mvr²(d) Fr
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the SI unit of moment of inertia.
8.Write the relation between torque and angular acceleration.
9.Write the moment of inertia of a ring of mass M and radius R about its central axis.
10.Define the centre of mass of a body.
11.Write the relation between angular momentum L and moment of inertia I.
12.State the parallel axis theorem.
13.Write the moment of inertia of a disc of mass M and radius R about its central axis.
14.Define angular momentum.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A torque of 4 N m produces an angular acceleration of 2 rad/s² on a body. Find its moment of inertia.
16.Find the moment of inertia of a ring of mass 2 kg and radius 0.5 m about its central axis.
17.A disc has a moment of inertia of 4 kg m² and is rotating at 5 rad/s. Find its angular momentum.
18.Two particles of masses 2 kg and 3 kg are placed at the origin and at x = 5 m respectively. Find the position of the centre of mass of the system.
19.A uniform rod of mass 3 kg and length 4 m is placed along the x-axis. Find the distance of its centre of mass from one end.
20.The moment of inertia of a disc of mass M and radius R about its central axis is MR²/2. If both the mass and the radius are doubled, by what factor does the moment of inertia increase?
Answer Key
1. b) The distribution of its mass about the axis of rotation
2. b) kg m²
3. a) Iα
4. b) MR²
5. b) Its midpoint
6. a) Iω
7. Refer to solution guide.
8. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
What does the moment of inertia depend on?
The distribution of mass about the axis of rotation, option (b) in this worksheet (Q1).
What is the SI unit of moment of inertia?
kg m², option (b) in this worksheet (Q2).
What is the moment of inertia of a ring of mass M and radius R?
MR², option (b) in this worksheet (Q4).
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