1. For a uniform rod with linear mass density lambda, what is the mass of a small element of length dx?
A.
lambda dx
B.
lambda/dx
C.
dx/lambda
D.
lambda + dx
Correct Answer:
lambda dx
Explanation:
The elemental mass is proportional to the elemental length and is given by dm = lambda dx.
2. A uniform rod of mass 4 kg and length 2 m has what linear mass density?
A.
2 kg/m
B.
8 kg/m
C.
0.5 kg/m
D.
6 kg/m
Correct Answer:
2 kg/m
Explanation:
The linear mass density is lambda = M/L = 4/2 = 2 kg/m.
3. A uniform rod has linear mass density 3 kg/m. What is the mass of a 0.2 m element of the rod?
A.
0.6 kg
B.
3.2 kg
C.
15 kg
D.
2.8 kg
Correct Answer:
0.6 kg
Explanation:
Using dm = lambda dx, the elemental mass is dm = 3 x 0.2 = 0.6 kg.
4. If a uniform rod of total mass M 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:
Equal divisions of a uniform rod have equal masses, so the mass of each element is the total mass divided by n.
5. For a uniform rod of length L and mass M, what is the mass of an element of length dx?
A.
(M/L)dx
B.
(L/M)dx
C.
ML dx
D.
M + L dx
Correct Answer:
(M/L)dx
Explanation:
The rod's linear mass density is M/L, so its elemental mass is dm = (M/L)dx.
6. What is the SI unit of linear mass density of a uniform rod?
A.
kg/m
B.
kg m
C.
m/kg
D.
kg/m^2
Correct Answer:
kg/m
Explanation:
Linear mass density is mass per unit length, so its SI unit is kilogram per metre, kg/m.
7. A uniform rod has total mass 10 kg and length 5 m. What is the mass of a 1 m length of the rod?
A.
2 kg
B.
5 kg
C.
10 kg
D.
50 kg
Correct Answer:
2 kg
Explanation:
The linear mass density is 10/5 = 2 kg/m, so a 1 m element has mass 2 kg.
8. For a uniform rod, how does the elemental mass dm depend on the elemental length dx?
A.
It is directly proportional to dx
B.
It is inversely proportional to dx
C.
It is independent of dx
D.
It is proportional to dx squared
Correct Answer:
It is directly proportional to dx
Explanation:
For a uniform rod, dm = lambda dx, so the elemental mass is directly proportional to the elemental length.
9. A uniform rod has mass 6 kg and length 3 m. What is the mass of an element of length 0.5 m?
A.
1 kg
B.
2 kg
C.
3 kg
D.
0.5 kg
Correct Answer:
1 kg
Explanation:
The linear mass density is lambda = 6/3 = 2 kg/m. Therefore, dm = 2 x 0.5 = 1 kg.
Short questions are currently unavailable for this page.