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Question

One fourth length of a uniform rod of length 2l and mass m is placed on a horizontal table and the rod is held horizontal. The rod is released from rest. If the normal reaction on the rod as soon as the rod is released is 4mgx, find the value of x.
156662_aeacb5dc3ab545c4b6c32489e855a40f.png

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Solution

The torque applied by gravity about the edge O=τ=mg(3l4)
I0α= 34mg ....(i)
where I0 = Ig+m(3l4)2
= ml212+916ml2
= ml24(13+94)
I0= 31ml248 .....(ii)

(i) and (ii) yield,

α= 3gml/431ml2/48
Newton's second law of motion,
mgN=ma - (iv)
Kinematics: a= (3l4)α - (v)
Using (iv) and (v) we obtain
N=mgm(27g31) N= 4mg31

231537_156662_ans_9ebdc1e9a87541f98dba98a76c802adf.png

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