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=10m/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 A8.5 rad/s2 Given: m1=5 kg and m2=2 kg l=1 m
τ=r×F=Iα Taking anticlockwise moment as positive, ⇒l2×m1g−l2×m2g=Iα ⇒12×5×g−12×2×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