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4 point size steel spheres each of mass $1 k g$ are placed on a turn table and are connected by 4 strings each of length $a$ to form a square. If the spheres are rotated with an angular velocity of $\frac{1}{2 π} rev / \sec$ , the tension in the connecting strings in newton is

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$\frac{a}{2}$

$\sqrt{2} a$

$a$

$\frac{a}{\sqrt{2}}$

answer is B.

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Detailed Solution

$\cos 45^{\circ} = \frac{a / 2}{r} \Rightarrow r = \frac{a}{\sqrt{2}}$

$ω = 2 π f = 2 π \times \frac{1}{2 π} = 1 rad / s$

$\sqrt{2} T = m ω r^{2}; \sqrt{2} T = 1 \times 1 \times \frac{a}{\sqrt{2}} \Rightarrow T = \frac{a}{2}$

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