1. A uniform rod has mass M and length L. What is its mass per unit length?
A.
M/L
B.
ML
C.
L/M
D.
M + L
Correct Answer:
M/L
Explanation:
For a uniform rod, the linear mass density is constant and is given by total mass divided by total length, λ = M/L.
2. For a uniform rod with linear mass density λ, what is the mass of a small element of length dx?
A.
λ/dx
B.
λ dx
C.
dx/λ
D.
λ + dx
Correct Answer:
λ dx
Explanation:
The elemental mass is obtained by multiplying linear mass density by the small length: dm = λ dx.
3. A uniform rod of mass 4 kg and length 2 m has what linear mass density?
A.
0.5 kg/m
B.
2 kg/m
C.
4 kg/m
D.
8 kg/m
Correct Answer:
2 kg/m
Explanation:
The linear mass density is λ = M/L = 4 kg ÷ 2 m = 2 kg/m.
4. A uniform rod has total mass 6 kg and length 3 m. What is the mass of a small element of length dx?
A.
2 dx kg
B.
3 dx kg
C.
6 dx kg
D.
18 dx kg
Correct Answer:
2 dx kg
Explanation:
The rod's linear mass density is λ = 6/3 = 2 kg/m. Therefore, the elemental mass is dm = λ dx = 2 dx kg.
5. If a uniform rod of length L is divided into n equal small elements, what is the length of each element?
A.
nL
B.
L/n
C.
L + n
D.
n/L
Correct Answer:
L/n
Explanation:
Dividing the total length L into n equal parts gives the length of each element as dx = L/n.
6. A uniform rod has mass M and is divided into n equal elements. What is the mass of each element?
A.
M/n
B.
nM
C.
M + n
D.
n/M
Correct Answer:
M/n
Explanation:
Since the rod is uniform, its mass is distributed equally among equal-length elements. Thus, each element has mass M/n.
7. Which expression represents the elemental mass of a uniform rod when its linear mass density is λ and the element extends from x to x + dx?
A.
dm = λx
B.
dm = λ dx
C.
dm = x dx
D.
dm = λ + dx
Correct Answer:
dm = λ dx
Explanation:
For a rod with constant linear mass density, the mass of a small length dx is dm = λ dx.
8. For a uniform rod, the linear mass density is expressed as which ratio?
A.
Length divided by mass
B.
Mass divided by length
C.
Mass multiplied by length
D.
Mass added to length
Correct Answer:
Mass divided by length
Explanation:
Linear mass density is defined as mass per unit length, so λ = M/L.
9. A uniform rod has linear mass density 3 kg/m. What is the mass of a 0.5 m section of the rod?
A.
0.5 kg
B.
1.0 kg
C.
1.5 kg
D.
6.0 kg
Correct Answer:
1.5 kg
Explanation:
The mass of a section is the product of linear mass density and its length: m = λl = 3 × 0.5 = 1.5 kg.
10. A uniform rod has mass M and length L. What is its linear mass density?
A.
M/L
B.
ML
C.
L/M
D.
M + L
Correct Answer:
M/L
Explanation:
For a uniform rod, linear mass density is the mass per unit length, so lambda = M/L.
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