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Question

Two balls of masses m1=1 kg and m2=2 kg are attached to a massless rod of length (l=1 m). Two parallel forces having equal magnitude of F=1 N, opposite in direction (couple) are acting on both the balls as shown in the figure. Find the angular acceleration of the system (α) about an axis passing through mid-point of the rod and also perpendicular to the plane of the rod. (Take anti-clockwise rotation as +ve)


A
23 rad/s2
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B
43 rad/s2
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C
13 rad/s2
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D
16 rad/s2
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Solution

The correct option is B 43 rad/s2
(Taking anti-clockwise rotation as +ve)
We know that,
Torque due to couple,
τ= Force × perpendicular distance between the two forces
τ=F×l
τ=1 Nm

Moment of inertia of system about the given axis,
I=m1r21+m2r22
I=1×(l2)2+2×(l2)2
=1×(12)2+2×(12)2=34 kgm2
Now, we also know,
τ=Iα
α=τI=134
α=43 rad/s2

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