A uniform rod AB of mass m and length L is suspended by two strings C and D of negligible mass as shown in the figure. When string D is cut, the tension in string C will be

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A uniform rod AB of mass m and length L is suspended by two strings C and D of negligible mass as shown in the figure. When string D is cut, the tension in string C will be

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$\frac{mg}{4}$

2mg

4mg

answer is A.

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Detailed Solution

$\begin{array}{l} mg - T = ma \\ τ = mg \cdot \frac{ℓ}{2} \\ α = \frac{τ}{I} = \frac{3 g}{2 ℓ} \\ a = \frac{Lα}{2} \\ mg - T = \frac{3 mg}{4} \\ T = \frac{mg}{4} \end{array}$