2021 A/L Physics Past Paper · Question 01 (English Medium)

Answer: (2) Work and energy

What the question asks

Find the pair of quantities that have the same dimensions.

We write the dimensions of both quantities of each pair in $M$, $L$, $T$.

Relevant theory

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

The unit of measurement of energy is the joule (J), the same as the unit of work.

The work done is force times distance.

$$[W] = [F \times s] = MLT^{-2} \times L = ML^2T^{-2}$$

Energy has the same unit as work. So it has the same dimensions.

$$[E] = ML^2T^{-2}$$

Reading the options

Only one pair has two equal dimensions.

asked

[A] = [B]

$a pair with equal dimensions$

1

M L^{-1} T^{-2} and 1

$stress, strain$

2

M L^2 T^{-2} and M L^2 T^{-2}

$work, energy$

3

L T^{-1} and L

$velocity, displacement$

4

M L T^{-2} and M

$weight, mass$

5

M L^2 T^{-2} and M L^2 T^{-1}

$torque, angular momentum$

Option (1): $ML^{-1}T^{-2}$ and no dimensions. These are different.

Option (3): $LT^{-1}$ and $L$. These are different.

Option (4): $MLT^{-2}$ and $M$. These are different.

Option (5): $ML^2T^{-2}$ and $ML^2T^{-1}$. These are different.

Only option (2) is left.

Checks

A quick check. Dimension check:

Work is the energy transferred by a force.

$$[W] = [E] = ML^2T^{-2}$$

Kinetic energy gives the same.

$$\left[\tfrac{1}{2}mv^2\right] = M \times (LT^{-1})^2 = ML^2T^{-2}$$

A quick check. Unit check:

Both are in joules.

$$\text{J} = \text{kg m}^2\text{ s}^{-2}$$

This matches $ML^2T^{-2}$.

Conclusion

$[W] = [E] = ML^2T^{-2}$

Work and energy both have the dimensions $ML^2T^{-2}$.

Does it make sense? Yes, the other four pairs differ. The answer is (2).

Torque and work have the same dimensions, $ML^2T^{-2}$, but they are different quantities.

The question asks about dimensions only. So check each pair on its own.

Exam tip