a bead of mass m is fitted on to a rodwith a length of 2l, and can move n it with friction having the coeff of frictionμ. at the initial moment the bead is in the middle of the rod. the rod moves translatory in a horizontal plane with an acceleration a in the direction forming an angle alpha with the rod find the time when the bead will leave the rod. (neglect the weight of the bead)


A pseudo force -ma acts on the bead. The frictional force,
f=μmasinα
The acceleration of the bead along the rod,
a0=macosα-μmasinαm=acosα-μasinα
So, the time after which the bead will fall off the rod,
t=2la0=2lacosα-μsinα
 

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