Vidaara.orgClass 11 · Physics
CodeVID-P11-06-COM-01
Centre of Mass — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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
5 × 1 = 5 marks
1.
The CM of a system depends on:
- A.only positions
- B.only masses
- C.both masses and positions
- D.neither
2.
Total momentum of a system equals:
- A.$M\vec{a}_{cm}$
- B.$M\vec{v}_{cm}$
- C.$\sum m_i$
- D.$\vec{r}_{cm}$
3.
Internal forces of a system:
- A.change the CM motion
- B.cancel in pairs
- C.add to gravity
- D.are always zero individually
4.
The CM of a uniform disc is at:
- A.the rim
- B.its centre
- C.the edge
- D.a focus
5.
If $\vec{F}_{ext}=0$, the CM:
- A.accelerates
- B.moves with constant velocity
- C.stops
- D.spins
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
Masses 1 kg and 3 kg lie at $x=0$ and $x=8$ m. Find the CM.
7.
State the relation between total momentum and CM velocity.
8.
Why can the CM of a ring lie outside the material?
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Masses 2 kg at $(0,0)$, 2 kg at $(4,0)$ and 4 kg at $(0,3)$ m. Find the CM.
10.
A 3 kg body at rest splits into 1 kg and 2 kg pieces; the 1 kg flies at $4\ \text{m/s}$. Find the 2 kg piece's speed.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Derive $M\vec{a}_{cm}=\vec{F}_{ext}$ for a two-particle system and explain why a projectile's CM follows a parabola even after it explodes.
Answer Key
Section A — Multiple Choice Questions
- (C) both masses and positions
- (B) $M\vec{v}_{cm}$
- (B) cancel in pairs
- (B) its centre
- (B) moves with constant velocity
Section B — Short Answer (2 marks)
- $x_{cm}=6\ \text{m}$.
- $\vec{P}=M\vec{v}_{cm}$.
- By symmetry the CM is at the geometric centre, which is empty space.
Section C — Short Answer (3 marks)
- $(1,\ 1.5)\ \text{m}$.
- $2\ \text{m/s}$ in the opposite direction.
Section D — Long Answer (5 marks)
- Adding the two equations of motion, internal forces cancel by Newton's third law, leaving $M\vec{a}_{cm}=\vec{F}_{ext}$; for a projectile the only external force is gravity, so the CM keeps its parabolic path.
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