CAIE A-Level Physics Algebra, Models and Dimensional Consistency

Practise rearranging linked physics equations, substituting consistent units and checking dimensions, percentages, symbols and quadratic solutions when the model requires them.

Exam points

change the subject of a physical equation and substitute values with consistent units
derive or check SI base units and dimensions of a quantity from a formula
rearrange simple physical relationships and interpret the resulting symbols

[Maximum number: 3]

A simple pendulum consists of a metal sphere suspended from a fixed point by means of a thread, as illustrated in Fig. 3.1.

Fig. 3.1 (not to scale)

The sphere of mass 94.0 g is displaced to one side through a horizontal distance of 12.7 cm . The centre of gravity of the sphere rises vertically by 0.90 cm .

The sphere is released so that it oscillates. The sphere may be assumed to oscillate with simple harmonic motion.

The period T of oscillation of the pendulum is given by the expression

T=2 \pi \sqrt{\left(\frac{L}{g}\right)}

where g is the acceleration of free fall and L is the length of the pendulum.
Use data from (b) to determine L.

$T=2 \pi / \omega$

C1

$2 \pi / 3.3=2 \pi \times(L / 9.81)^{1 / 2}$

C1

$L=0.90 \mathrm{~m}$

A1

All question bank results loaded

M.2-Algebra, models, units and dimensional consistency question 1