| Date | May 2016 | Marks available | 3 | Reference code | 16M.2.HL.TZ0.2 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | Calculate | Question number | 2 | Adapted from | N/A |
Question
The diagram shows a planet near two stars of equal mass M.
Each star has mass M=2.0×1030kg. Their centres are separated by a distance of 6.8×1011m. The planet is at a distance of 6.0×1011m from each star.
On the diagram above, draw two arrows to show the gravitational field strength at the position of the planet due to each of the stars.
Calculate the magnitude and state the direction of the resultant gravitational field strength at the position of the planet.
Markscheme
two arrows each along the line connecting the planet to its star AND directed towards each star
arrow lines straight and of equal length
Do not allow kinked, fuzzy curved lines.
\(g = \ll \frac{{GM}}{{{r^2}}} = \frac{{6.67 \times {{10}^{ - 11}} \times 2.0 \times {{10}^{30}}}}{{{{\left( {6.0 \times {{10}^{11}}} \right)}^2}}} \gg \) OR 3.7×10-4Nkg-1
\({g_{{\rm{net}}}} = \ll 2g\cos \theta = 2 \times 3.7 \times {10^{ - 4}} \times \frac{{\sqrt {{{6.0}^2} - {{3.4}^2}} }}{{6.0}} = \gg 6.1 \times {10^{ - 4}}{\rm{Nk}}{{\rm{g}}^{ - 1}}\)
directed vertically down «page» OR towards midpoint between two stars OR south
Allow rounding errors.
