Physics Assessment Questions on “Dimensional Formulae and Equations”.
1. [MLT-2] matches with the dimensional formula of ____
a) Force
b) Modulus of elasticity
c) Displacement
d) Strain
Answer: a
Clarification: The given dimensional formula matches with that of force. Force = mass x acceleration.
2. What is the maximum number of unknowns that can be found through a simple dimensional equation?
a) 6
b) 5
c) 3
d) 2
Answer: c
Clarification: A simple dimensional equation uses three basic parameters – mass, length and time. Hence the maximum number of unknowns that can be found is 3.
3. If, v stands for velocity, L for length, T for time and M for mass, what is the value of x in the equation –
L = (vT/M)x?
a) 3
b) 2
c) 1
d) 0
Answer: d
Clarification: The dimensions of velocity are LT-1. The dimensions of the RHS are LM-x and that of LHS is L. hence on equating we get x = 0.
4. Assuming standard notations, which of the following quantities is dimensionless?
a) v/a
b) P/Fv
c) FE/L
d) V2/g
Answer: b
Clarification: P/Fv is a dimensionless quantity. This is because, power(P) = Force(F) x Instantaneous Velocity(v).
5. If the units of length and time are doubled, what will be the factor by which the unit of acceleration will change?
a) 1
b) 0.25
c) 0.5
d) 2
Answer: c
Clarification: The dimensions of acceleration are LT-2. On doubling both length and time, the new dimensions become (0.5)*LT-2.
6. What are the dimensions of a light year?
a) L
b) T
c) LT-1
d) M
Answer: a
Clarification: Lightyear is the unit of measurement of distance; hence it has the dimensions of distance. Lightyear is the distance travelled by light in one year. It finds its use mostly in astronomy.
7. What are the dimensions of coefficient of friction?
a) MLT-2
b) LT-1
c) L
d) It is dimensionless
Answer: d
Clarification: Coefficient of friction is the ratio of Frictional force to Normal Reaction force; hence it is dimensionless. The formula for calculating this is, f = µN.
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