One endof a lightrod isclamped in sucha mannerthat rodcan be rotatedin a verticalplane . A blockof mass mis attached to the otherenedof rodandtheblockstaysat rest at its lowest position . What minimum speed should beimparted to thebockso that itmay complete itscircle ? Assume length of rod to be l .

One endof a lightrod isclamped in sucha mannerthat rodcan be rotatedin

1.	One endof a lightrod isclamped in sucha mannerthat rodcan be rotatedin a verticalplane . A blockof mass mis attached to the otherenedof rodandtheblockstaysat rest at its lowest position . What minimum speed should beimparted to thebockso that itmay complete itscircle ? Assume length of rod to be l .
Answer» Solution :This is a case of rodhencethere is no chance of losingcircularpath dueto slackness as in case of STRING . KINETICENERGY at the bottom SHOULDBE enough that block just reaches the top most position which is at a height 2l from bottom POINT . Force applied by the rod remains along teh LENGTH displacementsi perpendicularto that hence no workis done by this force . Only workdone by weight is involvedso systemis conservative .Let v be the speedof blockat lowest point. Loss in kineticenergy = gain gravitational potential energy `rArr"" 1/2 mv^(2) = mg(2l)` `rArr "" v = sqrt(4gl)`