Give an example of

(a) A physical quantity which has a unit but no dimensions

(b) A physical quantity which has neither unit nor dimensions

(c) A constant which has a unit

(d) A constant which has no unit

(a) A physical quantity which has a unit but no dimension is the angle.

Angle is dimensionless quantity, since:

[ ] is the notation used for dimension.

Hence, the angle is dimensionless quantity.

SI Unit of angle is Radians (rad).

(b) A physical quantity which has neither unit nor dimension is a strain.

The strain is dimensionless quantity.

Also, the strain has no unit.

(c) A constant which has a unit is the speed of light in a vacuum (c)

We know that the speed of light in vacuum is a constant, value given below

And has a unit of meter per second that is the unit of speed.

(d) A constant which has no unit is proton to electron mass ratio.

In physics, the dimensionless physical constant has no units.

Dimension:

Hence is dimensionless and also is unit less.

Now, kg

And kg

So,

Hence proton to electron mass ratio is dimensionless constant along with no unit.