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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. Find the normal reaction on the rod as soon as the rod is released


A

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B

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C

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D

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Solution

The correct option is C


The torque applied by gravity about the edge O=T=mg(314)

Io=34mgl ...(i) where Ig+m(3l4)2=ml212+916ml2=ml24(13+94)Io=31ml248 ...(ii)




(i) And (ii) yield, =3mgl431ml248 =144g124l=36g31l ....(iii)

Newton's second law of motion : mg - N = ma

Kinematics: α=(3l4)=36g31
Using (iii) & (iv) we obtain, N=mgm(27g31)N=4mg27.


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