One end of a uniform rod of mass m and cross-sectional area A is suspended from a rigid support and an equal mass m is suspended from the other end. The stress at the mid-point of the rod will be

Q: One end of a uniform rod of mass m and cross-sectional area A is suspended from a rigid support and an equal mass m is suspended from the other end. The stress at the mid-point of the rod will be

(a) 2mg/(A )

(b) 3mg/(2A )

(c) mg/(A )

(d) None of these

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Ans: (b)
Sol: Tension at the mid Point , $\displaystyle T = (m + \frac{m}{2}) g $

$\displaystyle T = \frac{3 m g}{2} $

$\displaystyle Stress = \frac{T}{A} $

$\displaystyle Stress = \frac{ 3 m g}{2 A} $