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Offline Centres

Q.

A body centred cubic arrangement is shown: O is the body centre; A, B, C, D, ....., H are the corners. What is the magnitude of the angle AOB?

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a

120°

b

109°28'

c

104°31'

d

70°32'

answer is D.

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Detailed Solution

$\begin{array}{l} AO = OB = \frac{\sqrt{3}}{2} a = ℓ \\ ∴ a^{2} = 2 ℓ^{2} - 2 ℓ^{2} \cos θ \\ a^{2} = 2 ℓ^{2} (1 - \cos θ) \\ a^{2} = \frac{3}{2} a^{2} (1 - \cos θ) \\ ∴ 1 - \cos θ = \frac{2}{3} \\ \cos θ = \frac{1}{3}, ∴ θ = 70^{\circ} 32^{'} \end{array}$

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