According to the conservation of momentum, we can write
mv−Mu=0,M=muv=0.60.052v=11.5v.This is the mass of the crate in terms of the mass of the block.
Next, apply the conservation of energy:
21mv+21Mu=9 J, 21⋅0.6v2+21M⋅0.0522=9 J, substitute M that we obtained from momentum, conservation:
21⋅0.6v2+2111.5v⋅0.0522=9 J,v=5.45 m/s (take the positive root).
Now substitute this velocity to the equation for M obtained from momentum conservation:
M=11.5⋅5.45=62.7 kg. The moment of inertia is
I=MR2, where R - the radius of the crate.
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