Question 1

Paper 2Medium12 marks

A probe is outside a spherical asteroid of uniform density. The asteroid has radius 4.0×105 m4.0\times10^5\ \mathrm{m} The probe has mass 800 kg800\ \mathrm{kg} Figure 1 shows the meaning of rr and measured values of the gravitational force FF on the probe at different distances from the asteroid’s centre.

ORPrMeasured gravitational force on the probe4567891002468101214r/(105 m)F/N

The gravitational constant is G=6.67×10−11 N m2 kg−2G=6.67\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}

(a)

State how the asteroid’s mass is treated when calculating the gravitational force on the probe.

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(b)

Use Figure 1 to state the measured gravitational force when r=6.0×105 mr=6.0\times10^5\ \mathrm{m}

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(c)

Use this measurement to estimate the mass of the asteroid.

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(d)

Using your estimate from (c), calculate the gravitational force on the 800 kg800\ \mathrm{kg} probe when r=8.0×105 mr=8.0\times10^5\ \mathrm{m} State whether this result agrees with Figure 1.

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(e)

At r=8.0×105 mr=8.0\times10^5\ \mathrm{m} a second probe has a mass of 1.6×103 kg1.6\times10^3\ \mathrm{kg} Determine the gravitational force on this probe.

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(f)

A student suggests that the readings at r=6.0×105 mr=6.0\times10^5\ \mathrm{m} and r=8.0×105 mr=8.0\times10^5\ \mathrm{m} are consistent with F∝1/rF\propto 1/r Use these readings to assess the suggestion.

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