QCEVault

Gravity and motion — Question 230

Original QCE Vault practice · 4 marks

Q230 · Practice questionComplex familiar4 marks

QUESTION 230 (4 marks)

The graph shows gravitational field strength g outside a spherical planet against 1/r21/r^2, where r is distance from its centre. The exact fitted line passes through (1.00×10−14 m−2,4.00 N kg−1)(1.00\times10^{-14}\,\mathrm{m^{-2}},4.00\,\mathrm{N\,kg^{-1}}). Use G=6.67×10−11 N m2 kg−2G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}.
Gravitational field strength in N/kg against inverse square radius in units of 10 to the minus 14 inverse square metres. A straight line through the origin passes through displayed coordinates (0.5,2), (1,4), (1.5,6) and (2,8).
a)
Determine the planet's mass from the gradient.
[2 marks]
b)
Determine the centre-to-point distance at which g=2.00 N kg−1g=2.00\,\mathrm{N\,kg^{-1}}.
[2 marks]
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