Gravitational Fields Structured Questions
Q3.
(a)
(i) Explain what is meant by the gravitational field strength at a point in a gravitational field.
The gravitational field strength at a point is the force per unit mass acting on a small test mass placed at that point in the field. ![](../../../graphics/symbols/nuclides/ticksmall.png)
(ii) State the SI unit of gravitational field strength.
N kg−1 ![](../../../graphics/symbols/nuclides/ticksmall.png)
(2 marks)
(b) Planet P has mass M and radius R. Planet Q has a radius 3R. The values of the gravitational field strengths at the surfaces of P and Q are the same.
(i) Determine the mass of Q in terms of M.
gP = gQ and G is a constant
so Mp/rp2 = Mq/rq2![](../../../graphics/symbols/nuclides/ticksmall.png)
Mq = Mprq2/rp2
Mp = M
rq = 3R
rp = R
Mq = M(3R)2/R2 ![](../../../graphics/symbols/nuclides/ticksmall.png)
Mq = 9M![](../../../graphics/symbols/nuclides/ticksmall.png)
(ii) The graph shows how the gravitational field strength above the surface of planet P varies with distance from its centre.
![](q3ANS.png)
An a line to the graph to show the variation of the gravitational field strength above the surface of Q over the range shown.
Graph line
- starts at 3R, with same initial value of g as existing curve
![](../../../graphics/symbols/nuclides/ticksmall.png)
- is a curve of decreasing negative gradient
![](../../../graphics/symbols/nuclides/ticksmall.png)
- shows the correct inverse square relationship,
![](../../../graphics/symbols/nuclides/ticksmall.png)
(6 marks)
(Total 8 marks)