Question 1

Paper 2Easy6 marks

A probe is outside a small spherical moon. Figure 1 shows the gravitational potential VgV_g as a function of distance rr from the moon’s centre. The positive radial direction is defined to be away from the moon. The radial component of gravitational field strength is related to the potential gradient by

gr=−ΔVgΔr.g_r=-\frac{\Delta V_g}{\Delta r}.
1.51.61.71.81.922.12.22.32.42.5-2.8-2.6-2.4-2.2-2-1.8-1.6-1.4r / (106 m)Vg / (106 J kg-1)
(a)

Read the graph and state VgV_g at r=2.0×106 mr=2.0\times10^6\ \mathrm{m} and r=2.5×106 mr=2.5\times10^6\ \mathrm{m}

[2]
(b)

Calculate the magnitude of the average radial gravitational field strength between these two distances.

[3]
(c)

State the direction of the gravitational field relative to the moon.

[1]

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