physics : class11 Coordinate System Selection : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
Practice important
Coordinate System Selection
MCQ questions and answers.
Page 1
of
2
|
20
MCQ Questions
1. For finding the centre of mass of a uniform straight rod, which coordinate axis is most convenient to place along the rod?
A.
The x-axis
B.
The y-axis only
C.
The z-axis only
D.
An axis perpendicular to the rod at one end
Correct Answer:
The x-axis
Explanation:
Placing the x-axis along the rod makes the position of every small element easy to describe using one coordinate.
2. A uniform rod of length L is placed along the x-axis from x = 0 to x = L. What are the coordinates of its ends?
A.
(0, 0) and (L, 0)
B.
(0, L) and (0, 0)
C.
(L, L) and (0, L)
D.
(-L, 0) and (0, 0)
Correct Answer:
(0, 0) and (L, 0)
Explanation:
Since the rod lies along the x-axis, its y-coordinate is zero, and its ends are at x = 0 and x = L.
3. A uniform rod of length L is placed along the x-axis with its midpoint at the origin. What are the coordinates of its ends?
A.
(0, L) and (0, -L)
B.
(L/2, 0) and (-L/2, 0)
C.
(L, 0) and (0, 0)
D.
(-L, -L) and (L, L)
Correct Answer:
(L/2, 0) and (-L/2, 0)
Explanation:
If the midpoint is at the origin and the rod lies along the x-axis, each end is L/2 from the origin in opposite x-directions.
4. For a uniform rod placed along the x-axis from x = 0 to x = L, which coordinate system choice makes the centre-of-mass position easiest to identify?
A.
Origin at one end of the rod
B.
Origin far from the rod with the rod at an angle
C.
Origin on the y-axis away from the rod
D.
Origin at a point outside the plane of the rod
Correct Answer:
Origin at one end of the rod
Explanation:
With the origin at one end and the x-axis along the rod, the rod extends simply from 0 to L, making its midpoint coordinate easy to determine.
5. A uniform rod lies along the y-axis from y = 0 to y = L. Which coordinate gives the position of a point on the rod?
A.
(x, 0)
B.
(0, y)
C.
(y, y)
D.
(L, y)
Correct Answer:
(0, y)
Explanation:
Every point on a rod lying along the y-axis has x-coordinate zero and is specified by its y-coordinate.
6. A uniform rod lies along the x-axis from x = -L/2 to x = L/2. Why is this coordinate choice convenient for locating its centre of mass?
A.
The rod has no length in this system
B.
The midpoint of the rod is at the origin
C.
Both ends have positive coordinates
D.
The rod becomes perpendicular to the x-axis
Correct Answer:
The midpoint of the rod is at the origin
Explanation:
Choosing equal and opposite coordinates for the ends places the geometric midpoint, and hence the centre of mass, at the origin.
7. A uniform rod of length 2 m is placed along the x-axis from x = 3 m to x = 5 m. Which coordinate system description is correct?
A.
The rod is centred at x = 0 m
B.
The rod is centred at x = 1 m
C.
The rod is centred at x = 4 m
D.
The rod is centred at x = 5 m
Correct Answer:
The rod is centred at x = 4 m
Explanation:
The midpoint coordinate is the average of the endpoint coordinates: (3 m + 5 m)/2 = 4 m.
8. When a uniform rod is horizontal on a table, which coordinate system is generally most suitable for analysing its centre of mass?
A.
The x-axis along the rod and the y-axis perpendicular to it
B.
Both axes perpendicular to the rod
C.
The x-axis vertical and the y-axis along the table edge only
D.
An origin chosen without reference to the rod
Correct Answer:
The x-axis along the rod and the y-axis perpendicular to it
Explanation:
Aligning one axis with the rod reduces the position of its elements to a single varying coordinate.
9. A uniform rod is placed along the x-axis from x = -2 m to x = 4 m. What coordinate represents its midpoint?
A.
x = -3 m
B.
x = -1 m
C.
x = 1 m
D.
x = 2 m
Correct Answer:
x = 1 m
Explanation:
The midpoint coordinate is the average of the endpoint coordinates: (-2 m + 4 m)/2 = 1 m.
10. If the origin is chosen at the centre of a uniform rod and the rod is placed along the x-axis, what are the coordinates of its centre of mass?
A.
(L, 0)
B.
(0, L)
C.
(0, 0)
D.
(L/2, L/2)
Correct Answer:
(0, 0)
Explanation:
For a uniform rod, the centre of mass is at its geometric centre. Choosing that point as the origin gives coordinates (0, 0).