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Q2. (a) The amount of energy stored in similar flywheels varies directly as the squares of their speeds and as the fifth power of their diameters.

A wheel, A, running its normal operating speed stores 8.2 kJ. Another similar wheel, B, has a diameter 1.7 times that of A and runs at 0.84 of the speed of A.

Determine the energy stored in B. (6)

(b) A cable 200 metres long has to be cut into FOUR lengths.

THREE of the lengths are to be equal and the fourth length must be 10 metres shorter than the sum of the equal lengths.

Calculate the fourth length. (6)

(c) The sag, y, at the centre of the wire, of length, l, supported at TWO points, distance d apart, is given by the formula:

y = √(3d(ℓ - d)/8)

Transpose the formula to make l the subject. (4)