4400 Higher June 2010 Paper 3 Q15
15 The light intensity, \(E\), at a surface is inversely proportional to the square of the distance, \(r\), of the surface from the light source.
\(E = 4\) when \(r = 50\)
(a) Express \(E\) in terms of \(r\). (3)
(b) Calculate the value of \(E\) when \(r = 20\) (1)
(c) Calculate the value of \(r\) when \(E = 1600\) (2)
| Scheme | Marks |
|---|---|
| \(E = \dfrac{k}{r^2}\) | M1 |
| \(4 = \dfrac{k}{50^2}\) | M1 |
| \(\dfrac{10000}{r^2}\) | A1 |
| (3) |
Notes
M1: for \(E = \dfrac{k}{r^2}\) but not for \(E = \dfrac{1}{r^2}\)
A1: Award 3 marks if answer is \(E = \dfrac{k}{r^2}\) but \(k\) is evaluated as 10 000 in any part
| Scheme | Marks |
|---|---|
| 25 | B1 |
| (1) |
Notes
B1: ft from \(\dfrac{\text{“}10000\text{”}}{400}\) except for \(k = 1\), if at least M1 scored in (a)
| Scheme | Marks |
|---|---|
| \(r^2 = \dfrac{10000}{1600}\) oe | M1 |
| 2.5 oe | A1 |
| (2) | |
| (6 marks) |
Notes
M1: for substitution and rearrangement into form \(r^2 = \dfrac{k}{1600}\) or \(r = \dfrac{\sqrt{k}}{40}\) with their value of \(k\) except for \(k = 1\)
A1: cao