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Question

5 balls of mass 1 kg,2 kg,3 kg,4 kg and 5 kg are tied in a horizontal plane with the massless rod as shown in figure. Balls are rotating about XX axis with constant angular velocity ω=10 rad/s. Find the magnitude of angular momentum [in kg m2/s] about axis XX.


A
750
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B
500
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C
2000
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D
1000
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Solution

The correct option is C 2000
As we know,
Lsystem=Iaxis.ω
Here, Iaxis=m1r21+m2r22+m3r23+m4r24+m5r25
Iaxis=1×22+2×42+3×12+4×32+5×52
Iaxis=4+32+3+36+125
Iaxis=200 kg m2
Hence,
Lsystem=Iaxis.ω
=200 kg-m2×10rads
=2000 kg-m2rads
i.e L=2000 kg-m2rads

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