Q#5 (Past Exam Paper – November 2016 Paper 42 Q1)
(a) Define gravitational field strength. [1]
(b) The nearest star to the Sun is Proxima Centauri.
This star has a mass of 2.5 × 1029 kg and is a distance of 4.0 × 1013 km from the Sun.
The Sun has a mass of 2.0 × 1030 kg.
(i) State why Proxima Centauri may be assumed to be a point mass when viewed from the Sun. [1]
(ii) Calculate
1. the gravitational field strength due to Proxima Centauri at a distance of 4.0 × 1013 km, [2]
2. the gravitational force of attraction between the Sun and Proxima Centauri. [2]
(c) Suggest quantitatively why it may be assumed that the Sun is isolated in space from other stars. [2]
[Total: 8]
Solution:
(a) Gravitational field strength is defined as the (gravitational) force acting per unit mass.
(b)
(i)
The radius/diameter/size of Proxima Centauri is much less than the separation (of the Sun and the star (Proxima Centauri)). (Separation = 4.0 × 1013 km)
OR
(because) it is a uniform sphere
(ii)
1.
field strength = GM / x2
{distance should be in metre.}
field strength = (6.67×10-11 × 2.5×1029) / (4.0×1013 × 103)2
field strength = 1.0 × 10-14 N kg-1
2.
{Force = mg}
force = field strength × mass
force = 1.0×10-14 × 2.0×1030
or
force = GMm / x2
force = (6.67×10-11 × 2.5×1029 × 2.0×1030) / (4.0×1013 × 103)2
force = 2.0 × 1016 N
(c)
The force (of 2 × 1016 N) would have little effect on the (large) mass of the Sun and would cause a negligible acceleration (of 1.0 × 10–14 m s–2).
OR
Many stars are all around the Sun. The net effect of the forces/fields is zero.
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