Q164 · Practice questionComplex unfamiliar5 marks
QUESTION 164 (5 marks)
Two isolated spherical bodies have masses and . Their centres are apart. Consider points on the line between them, outside both bodies. Their radii are small enough that the field-cancellation point is outside each body.
a)[3 marks]
Determine the distance from the centre of the body of mass at which the net gravitational field is zero.
b)[2 marks]
A small test mass is displaced a short distance from this point towards the body of mass and released from rest. Determine the direction of its initial acceleration and explain your reasoning.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) toward the other body. (b) Towards the body of mass , away from the field-cancellation point.
Worked solution
(a) The fields oppose between the bodies. Let be distance from and . Set . Taking positive square roots gives , hence .
(b) At the cancellation point the opposing fields have equal magnitudes. Moving towards decreases the distance to , increasing its field magnitude . It also increases the distance to , decreasing that opposing field. The resultant field, and hence the initial acceleration, points towards .
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Set opposing field magnitudes equal.
Part a: Solve the distance relationship using centre-to-centre distances.
Part a: Give the location from the smaller mass.
Part b: Identify initial acceleration towards the smaller body.
Part b: Explain that its field increases while the opposing field decreases under inverse-square scaling.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?
Compare your working with the guide above.