Question

A uniform rod of length l and mass m is suspended on two vertical inextensible strings as shown in the fig. Then tension T in the left string at the instant, when right string snaps it?



a) T = mg b) T = mg2 c) T = mg4 d) T = zero

Answer 1

Please find below the solution to the asked query:

When the right string snaps, then the rod starts rotating about the left string. Then the angular acceleration of the rod is,

Before snaping the string, the tension in the strings are,2T=mg
⇒T=mg2Torque on the rod is,τ=mg(l2)
⇒Iα=mgl2
⇒13ml2α=mgl2
⇒α=3g2lSo, the acceleration with which the centre of mass falls down is,a=lα2=3g4So, ma=Fdown−Fup⇒m3g4


ma=Fdown−Fup⇒m3g4=mg−T'⇒T'=mg−3mg4⇒T'=mg4