is it possible for two quantities to (a) have the same units but different dimensions or (b) have the same dimensions but different units? explain.

If two quantities have same units, they will be comprised of the same basic physical quantities and hence their dimensions will be same. Same dimensions do not represent the same physical quantity. For example, The kinetic energy and the potential energy are measured in the same units but they possess different physical quantities.

What is dimensions?

The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.

Two quantities with the same units will be made up of the same fundamental physical quantities, resulting in identical dimensions. The same physical quantity does not have the same dimensions. For instance, although having different physical properties, kinetic energy and potential energy are measured in the same units.

quantitieshave same units, they will be comprised of the same basic physical quantities and hence their dimensions will be same. Samedimensionsdo not represent the samephysicalquantity. For example, The kinetic energy and the potential energy are measured in the same units but they possess different physical quantities.## What is dimensions?

coordinatesrequired to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has adimensionof one because apointon it can be specified by a single coordinate, such as the point at 5 on a number line.quantitieswith the same units will be made up of the same fundamental physical quantities, resulting in identicaldimensions. The samephysicalquantity does not have the same dimensions. For instance, although having different physical properties, kinetic energy and potential energy are measured in the same units.dimensions,