Units and Measurements Test

Result

Units and Measurements Test - 8

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Weekly Quiz Competition

Question 1
4 / -1

Which of the following physical quantities has a unit but no dimensions?

A
Relative velocity

B
Relative density

C
Strain

D
Angle

Solution

Among the given physical quantities angle has a unit but no dimensions. Angle = [M°L°T°]
The SI unit of angle is radian.
Question 2
4 / -1

Which of the following physical quantities has neither units nor dimensions?

A
Relative velocity

B
Relative density

C
Angle

D
Energy

Solution

Relative density is the ratio of two like quantities.
Therefore, it has neither unit nor dimensions.
Question 3
4 / -1

A dimensionless quantity

A
never has a unit

B
always has unit

C
may have a unit

D
does not exit

Solution

A dimensionless quantity need not always have a unit, example: angular displacement, θ is dimensionless but has a unit of radians, and quantities like co-efficient of friction, have no dimensions and no units.
Question 4
4 / -1

Which of the following pairs of physical quantities have same dimensions?

A
Force and power

B
Torque and energy

C
Torque and power

D
Force and torque

Solution

we know, force = mass × acceleration
energy = Workdone = force × displacement
power = energy/time
torque = force × perpendicular distance between force and axis of rotation. now, by these formula, find dimension of all terms.
Example: dimension of force = [MLT⁻²]
dimension of energy = [ML²T⁻²]
dimension of power = [ML²T⁻³]
dimension of torque = [ML²T⁻²]
Here it is clear that dimension of energy and dimension of torque are equal.
Hence, option (b) is correct.
Question 5
4 / -1

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

A
(P - Q)/R

B
PQ - R

C
PQ/R

D
(PR - Q²)/R

Solution

Physical quantities having different dimensions cannot be added or subtracted.
As P, Q and R are physical quantities having different dimensions, therefore they can neither be added nor be subtracted.
Thus, (a) can never be a meaningful quantity.