Higher June 2023 Paper 1R Q17
17 \(F\) is inversely proportional to the square of \(r\)
\(F = 36\;\) when \(\;r = 4\)
(a) Find a formula for \(F\) in terms of \(r\) (3)
(b) Work out the value of \(F\) when \(\;r = 48\) (1)
| Scheme | Marks |
|---|---|
| \(F = \dfrac{k}{r^2}\) or \(kF = \dfrac{1}{r^2}\) | M1 |
| \(36 = \dfrac{k}{4^2}\) oe or \(k = 36 \times 4^2\) or \(k = 576\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(F = \dfrac{576}{r^2}\) | A1 |
| (3) |
Notes
M1: (NB. Not for \(F = \dfrac{1}{r^2}\))
Constant of proportionality must be a symbol such as \(k\)
M1: for substitution of \(F\) and \(r\) into a correct formula
A1: oe e.g \(F = 576(\times)\dfrac{1}{r^2}\)
Award 3 marks if answer is \(F = \dfrac{k}{r^2}\) on the answer line and \(k = 576\) clearly given in the body of working of the script
M2 for \(36 = \dfrac{k}{4^2}\) oe
| Scheme | Marks |
|---|---|
| 0.25 | A1ft |
| (1) | |
| (4 marks) |
Notes
A1ft: oe dep on M1 in part (a) and for their value of \(k\) if \(F = \dfrac{k}{r^2}\)