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Fuel of \( 4000 \ \mathrm{kg} \) burns from a tank \( 1.5 \ \mathrm{m} \) aft of the centre of gravity on an aeroplane of \( 40\,000 \ \mathrm{kg} \). The centre of gravity moves forward by approximately

  • A.0.15 m
  • B.1.5 m
  • C.0.60 m
  • D.0.167 m

Answer: D

Correct answer: 0.167 m

Removing a mass \( m \) at a distance \( d \) from the centre of gravity shifts it by \( m d \) divided by the mass that remains:

\[ \Delta x = \frac{4000 \times 1.5}{40\,000 - 4000} = \frac{6000}{36\,000} = 0.167 \text{ m} \]

The fuel was aft, so removing it draws the centre of gravity forward and the static margin increases. Dividing by the original 40,000 kg rather than the final 36,000 kg gives 0.15 m, which is the usual slip: the moment must be taken about the mass that is actually left.

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