4MA0 Higher January 2012 Paper 3 Q15
15 Two small magnets attract each other with a force, \(F\) newtons.
\(F\) is inversely proportional to the square of the distance, \(d\) cm, between them.
When \(d = 2\), \(F = 12\)
(a) Express \(F\) in terms of \(d\). (3)
(b) Calculate the value of \(F\) when \(d = 5\) (1)
(c) Calculate the value of \(d\) when \(F = 3\) (2)
| Scheme | Marks |
|---|---|
| \(F = \text{“}k\text{”}/d^2\) | M1 |
| \(12 = k/2^2\) | M1 |
| \(k = 48\) Answer: \(F = 48/d^2\) | A1 |
| (3) |
Notes
M1: \(k\) = letter not number.
A1: Award 3 marks for \(F = \text{“}k\text{”}/d^2\) and \(k = 48\) stated anywhere, unless contradicted by later work.
| Scheme | Marks |
|---|---|
| (\(F\) = ) “48”/ \(5^2\) Answer: 1.92 oe | B1 ft \(k \neq 1\) |
| (1) |
Notes
B1 ft \(k \neq 1\): accept 48/25 as an answer.
| Scheme | Marks |
|---|---|
| \(3 = \text{“}48\text{”}/d^2\) \(d^2 = \text{“}48\text{”}/3\) | M1 |
| 4 | A1 |
| (2) | |
| (Total 6 marks) |
Notes
M1: \(k \neq 1\)
Rearrangement to make \(d^2\) or \(d\) the subject
A1: ignore ±