question_answer

A horizontal heavy uniform bar of weight W is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

A)  w                                          

B)  w/2

C)  3w/4                                    

D)  w/4

Correct Answer: D

Solution :

                 Let us first consider linear acceleration of CG. When the man at B withdraws his support, the bar turns about A with an angular acceleration\[\alpha \]given by\[I\alpha =\frac{wl}{2}\]                                 As           \[I=\frac{m{{l}^{2}}}{3}\]and\[w=mg\]                 hence     \[\alpha =\frac{3g}{2l}\]                 Hence, linear acceleration of C.G,                 \[a=\frac{1}{2}\alpha =\frac{1}{2}\frac{3g}{2l}=\frac{3g}{4}\]                 Now, if normal reaction at A is N, then                 \[w-N=ma\Rightarrow mg-N=m\frac{3g}{4}\]                 \[\Rightarrow \]\[N=\frac{mg}{4}=w/4\]