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Question

A light rod of length l=1 m is hinged at its centre and two masses of m1=5 kg and m2=2 kg are hung from the ends as shown in figure. Find the initial angular acceleration of the rod assuming that it was horizontal in beginning. (Take g=10 m/s2)



A
8.5 rad/s2
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B
4.4 rad/s2
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C
3.4 rad/s2
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D
5.4 rad/s2
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Solution

The correct option is A 8.5 rad/s2
Given:
m1=5 kg and m2=2 kg
l=1 m


τ=r×F=Iα
Taking anticlockwise moment as positive,
l2×m1gl2×m2g=Iα
12×5×g12×2×g=Iα
3g2=Iα ....(i)

We know,
I=MR2=m1(l2)2+m2(l2)2 =5(12)2+2(12)2=74 kg-m2 ....(ii)
From equation (i) and (ii)
32×10=74α
α=8.5 rad/s2

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