Answer to Question #337555 in Mechanics | Relativity for Dammy

Question

A uniform rod 8m long weighing 5kg is supported horizontally by two vertical parallel strings at P and Q, and at distances of 2m and 6m from one end. Weights of 1kg, 1.5kg and 2kg are attached at distances of 1m, 5m and 7m respectively from the same end. Find the tension in each vertical string.

Answer 1

$T_1+T_2=(m_1+m_2+m_3+M)g=9.5g,\\ M_{\Sigma T}=M_{\Sigma m},\\ 2T_1+6T_2=(1\cdot1+4\cdot 5+5\cdot 1.5+7\cdot 2)g=42.5g,\\ T_1+T_2=9.5g,\\ T_1+3T_2=21.25g,\\ T_2=5.875g=57.6~N,\\ T_1=3.625g=35.5~N.$