One end of a uniform rod of mass m1, uniform area of cross-section A is suspended from the roof and mass m is suspended from the other end. What is the stress at the mid point of the rod?

Question

One end of a uniform rod of mass m1, uniform area of cross-section A is suspended from the roof and mass m is suspended from the other end. What is the stress at the mid point of the rod? (A) (m1+m2) g / A (B) (m1-m2) g / A (C) [((m1 / 2)+m2/A)] g (D) [(m1+(m2 / 2)/A)] g

Tardigrade Admin · Accepted Answer

As, stress =(. weight due to mass m2+ half of the weight of rod)/area =(m2 g+m1 g / 2) / A=[(m1 / 2)+m2] g / A

Q. One end of a uniform rod of mass $m_{1}$ , uniform area of cross-section $A$ is suspended from the roof and mass $m$ is suspended from the other end. What is the stress at the mid point of the rod?

$(m_{1} + m_{2}) g / A$

$(m_{1} - m_{2}) g / A$

$[\frac{( m _{1} /2 ) + m _{2}}{A}] g$

$[\frac{m _{1} + ( m _{2} /2 )}{A}] g$

As, stress $= ($ weight due to mass $m_{2} +$ half of the weight of rod)/area
$= (m_{2} g + m_{1} g /2) / A = [(m_{1} /2) + m_{2}] g / A$

Q. One end of a uniform rod of mass m1​, uniform area of cross-section A is suspended from the roof and mass m is suspended from the other end. What is the stress at the mid point of the rod?

(m1​+m2​)g/A

(m1​−m2​)g/A

[A(m1​/2)+m2​​]g

[Am1​+(m2​/2)​]g