2024 A/L Physics Past Paper · Question 01 (English Medium)

Answer: (5) Sound intensity level

What the question asks

We want: the quantity that has a unit but no dimension.

What each word means:

Unit: the name we give to the size of a measurement, such as the metre or the joule.

Dimension: the way the quantity is built from the basic quantities mass M, length L and time T.

Relevant theory

There are quantities with units but without dimensions.

Symbolic expressions which show the relation of a physical quantity to basic units is called its dimension.

Therefore, a quality called intensity level has been introduced to represent the above mentioned range. It is defined as follows. It's unit is decibel (dB).

The amount of work done is given by the product of the displacement of the point of action of the force and the force acting in that direction.

The first quote says that some quantities have a unit but no dimension, and gives a plane angle as an example. The second says what a dimension is. The third gives the sound intensity level, $\beta = 10\log_{10}\dfrac{I}{I_0}$, with the unit decibel. The fourth gives work as force times displacement, so we can find the dimension of energy.

Reading the options

For example, think of your marks in a test. You get $45$ marks out of $50$, so you get $90$ percent.

Marks divided by marks leaves a plain number. The word percent is just a label we write after it. No mass, length or time is left in it.

A quantity that is a ratio of two like quantities is like that. It can carry a unit name but it has no dimension.

The sound intensity level is a ratio too. It compares one sound intensity $I$ with a standard intensity $I_0$, and the decibel is its label.

Test each option against the quotes.

(1) Planck constant: $h = \dfrac{E}{f}$ has the dimension $\text{M}\text{L}^2\text{T}^{-1}$.

(2) Surface tension: the force on a unit length has the dimension $\text{M}\text{T}^{-2}$.

(3) Energy: the dimension is $\text{M}\text{L}^2\text{T}^{-2}$.

(4) Relative velocity: the dimension is $\text{L}\text{T}^{-1}$.

(5) Sound intensity level: a ratio of two intensities, so M, L and T cancel. It has no dimension, and its unit is the decibel.

Option (5) matches.

Why the other options fail

The Planck constant is written with M, L and T, as $\text{M}\text{L}^2\text{T}^{-1}$. A quantity written with the basic quantities has a dimension.

The surface tension is written with M and T, as $\text{M}\text{T}^{-2}$. So it has a dimension.

Energy is the same kind of quantity as work, which is force times displacement, $\text{M}\text{L}^2\text{T}^{-2}$. So it has a dimension.

A relative velocity is a displacement over a time, $\text{L}\text{T}^{-1}$. So it has a dimension.

Conclusion

The sound intensity level is a ratio of two intensities. It has the unit decibel but no dimension.

The answer is (5).

A ratio of two like quantities has no dimension. It may still carry a unit name, such as percent, radian or decibel.

To test a quantity, write its formula and see whether M, L and T cancel.

Exam tip