physics : class11 Dimensional Formula of Surface Energy : Surface Energy : Properties of Bulk Matter MCQ Questions and Answers
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Dimensional Formula of Surface Energy
MCQ questions and answers.
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MCQ Questions
1. The dimensional formula of surface energy per unit area is obtained by dividing the dimensional formula of energy by that of area. Which expression is correct?
A.
[M L^2 T^-2]
B.
[M L T^-2]
C.
[M T^-2]
D.
[M L^-1 T^-2]
Correct Answer:
[M T^-2]
Explanation:
Surface energy per unit area has dimensions of energy divided by area. Since energy is [M L^2 T^-2] and area is [L^2], the result is [M T^-2].
2. A quantity X is defined as the work required to increase the surface area of a liquid by unit area. What is the dimensional formula of X?
A.
[M L^2 T^-2]
B.
[M T^-2]
C.
[M L^-1 T^-2]
D.
[M L T^-1]
Correct Answer:
[M T^-2]
Explanation:
X is surface energy per unit area. Work has dimensions [M L^2 T^-2], and dividing by area [L^2] gives [M T^-2].
3. Which combination of fundamental quantities has the same dimensions as surface energy per unit area?
A.
Mass divided by time squared
B.
Mass multiplied by length divided by time squared
C.
Mass multiplied by length squared divided by time
D.
Mass divided by length multiplied by time squared
Correct Answer:
Mass divided by time squared
Explanation:
The dimensional formula of surface energy per unit area is [M T^-2], which corresponds to mass divided by time squared.
4. If surface energy per unit area is represented by S, which dimensional equation is valid?
A.
S = [M L^2 T^-2]
B.
S = [M L T^-2]
C.
S = [M T^-2]
D.
S = [M L^-2 T^2]
Correct Answer:
S = [M T^-2]
Explanation:
Surface energy per unit area equals energy divided by area. Therefore, S has dimensions [M L^2 T^-2][L^-2] = [M T^-2].
5. The surface energy density of a liquid is numerically expressed in joules per square metre. What is its dimensional formula?
A.
[M L^2 T^-2]
B.
[M L^-2 T^-2]
C.
[M T^-2]
D.
[M L^-1 T^-1]
Correct Answer:
[M T^-2]
Explanation:
One joule has dimensions [M L^2 T^-2]. Dividing by square metre, [L^2], gives [M T^-2].
6. A physical quantity has dimensions equal to force divided by length. Which dimensional formula does it share with surface energy per unit area?
A.
[M L T^-2]
B.
[M T^-2]
C.
[M L^-1 T^-2]
D.
[M L^2 T^-2]
Correct Answer:
[M T^-2]
Explanation:
Force has dimensions [M L T^-2]. Dividing by length [L] gives [M T^-2], the dimensional formula of surface energy per unit area.
7. Suppose a derived unit of mass is doubled, the unit of length is halved, and the unit of time is unchanged. How does the numerical value of a fixed surface energy per unit area change in the new system?
A.
It becomes half its original value
B.
It becomes twice its original value
C.
It becomes four times its original value
D.
It remains unchanged
Correct Answer:
It becomes half its original value
Explanation:
Surface energy per unit area has dimensions [M T^-2] and is independent of length. The new unit is twice the old unit because the mass unit is doubled, so the numerical value becomes half.
8. In a hypothetical unit system, the unit of mass is one-fourth of the SI mass unit and the unit of time is twice the SI time unit. What is the numerical value of a fixed surface energy per unit area compared with its SI numerical value?
A.
One-fourth
B.
One-half
C.
Four times
D.
Sixteen times
Correct Answer:
Sixteen times
Explanation:
The unit of surface energy per unit area has dimensions M T^-2. Its new unit is (1/4) times the mass unit multiplied by (2)^-2 for time, giving 1/16 of the SI unit. Hence the numerical value becomes sixteen times.
9. Which dimensional expression would make the equation E = S A dimensionally consistent, where E is energy, A is area, and S denotes surface energy per unit area?
A.
[S] = [M L^2 T^-2]
B.
[S] = [M L T^-2]
C.
[S] = [M T^-2]
D.
[S] = [M L^-2 T^2]
Correct Answer:
[S] = [M T^-2]
Explanation:
For E = S A, S must have dimensions [E]/[A] = [M L^2 T^-2]/[L^2] = [M T^-2].
10. A student claims that the dimensional formula of surface energy per unit area is [M L^-1 T^-2] because it is related to force per unit area. Which correction is valid?
A.
Surface energy per unit area is energy per unit area, so its dimensions are [M T^-2]
B.
Surface energy per unit area is force per unit area, so the student's result is correct
C.
Surface energy per unit area has dimensions [M L^2 T^-2] because it is a form of energy
D.
Surface energy per unit area has dimensions [M L T^-1] because it involves work
Correct Answer:
Surface energy per unit area is energy per unit area, so its dimensions are [M T^-2]
Explanation:
Surface energy per unit area is obtained from energy divided by area, giving [M T^-2]. Force per unit area has dimensions [M L^-1 T^-2] and is a different quantity.
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