Vidaara.orgClass 11 · Physics
CodeVID-P11-06-CH-01
System of Particles and Rotational Motion — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
6 × 1 = 6 marks
1.
The total momentum of a system equals:
- A.$M\vec{a}_{cm}$
- B.$M\vec{v}_{cm}$
- C.$M\vec{r}_{cm}$
- D.$\sum m_i$
2.
The SI unit of torque is:
- A.newton
- B.joule
- C.newton metre
- D.watt
3.
Moment of inertia of a solid sphere about a diameter is:
- A.$MR^2$
- B.$\frac{1}{2}MR^2$
- C.$\frac{2}{5}MR^2$
- D.$\frac{2}{3}MR^2$
4.
Angular momentum is:
- A.$I\alpha$
- B.$I\omega$
- C.$\frac{1}{2}I\omega^2$
- D.$\tau\theta$
5.
The rolling-without-slipping condition is:
- A.$v=\omega/R$
- B.$v=\omega R$
- C.$v=R/\omega$
- D.$a=\omega R$
6.
Rotational kinetic energy is:
- A.$\frac{1}{2}mv^2$
- B.$\frac{1}{2}I\omega^2$
- C.$I\omega$
- D.$\tau\omega$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
7.
Masses 2 kg and 6 kg lie at $x=0$ and $x=8$ m. Find the CM.
8.
A 30 N force acts perpendicular at 0.4 m from the axis. Find the torque.
9.
A disc with $I=0.5\ \text{kg m}^2$ spins at $6\ \text{rad/s}$. Find its angular momentum.
10.
A wheel of radius 0.5 m rolls without slipping at $4\ \text{m/s}$. Find $\omega$.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
11.
A 4 kg shell moving at $8\ \text{m/s}$ explodes into 1 kg and 3 kg pieces; the 1 kg flies forward at $20\ \text{m/s}$. Find the 3 kg piece's velocity.
12.
A solid cylinder of mass 2 kg, radius 0.1 m rotates about its axis. Find $I$ and its rotational KE at $\omega=10\ \text{rad/s}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
13.
Define moment of inertia and radius of gyration. State the law of conservation of angular momentum and explain it with the example of a spinning ice-skater.
14.
A solid sphere rolls without slipping from rest down an incline of height 1.4 m. Find its speed at the bottom and explain why it beats a ring. ($g=10\ \text{m/s}^2$)
Answer Key
Section A — Multiple Choice Questions
- (B) $M\vec{v}_{cm}$
- (C) newton metre
- (C) $\frac{2}{5}MR^2$
- (B) $I\omega$
- (B) $v=\omega R$
- (B) $\frac{1}{2}I\omega^2$
Section B — Short Answer (2 marks)
- $x_{cm}=6\ \text{m}$.
- $\tau=12\ \text{N m}$.
- $L=3\ \text{kg m}^2\text{/s}$.
- $\omega=8\ \text{rad/s}$.
Section C — Short Answer (3 marks)
- Momentum: $32=20+3v\Rightarrow v=4\ \text{m/s}$ forward.
- $I=0.01\ \text{kg m}^2$; $KE=0.5\ \text{J}$.
Section D — Long Answer (5 marks)
- $I=\sum m_i r_i^2$ and $I=Mk^2$ so $k=\sqrt{I/M}$; with zero external torque $L=I\omega$ is constant, so a skater pulling in the arms lowers $I$ and spins faster.
- $v=\sqrt{\frac{2(10)(1.4)}{1+2/5}}=\sqrt{20}\approx4.47\ \text{m/s}$; the sphere's smaller $k^2/R^2$ gives a larger acceleration, so it beats the ring.
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