A uniform stick of mass 18 kg and length 3 m spins around on a frictionless horizontal plane, with its Centre of Mass stationary. A mass M is placed on the plane, and the stick collides elastically wi

Question

A uniform stick of mass 18 kg and length 3 m spins around on a frictionless horizontal plane, with its Centre of Mass stationary. A mass M is placed on the plane, and the stick collides elastically with it, as shown (with the contact point being the end of the stick). What should M (in kg) be so that after the collision the stick has translational motion, but no rotational motion?

TestHub · Accepted Answer

(i) L i ​ = L f ​ ; 12 m l 2 ​ ω = M V × 2 l ​ ⇒ V = 6 M mω l ​ (ii) P i ​ = P f ​ ; 0 = M V − m V 1 ​ ⇒ V = M m V 1 ​ ​ ⇒ 6 ω l ​ = V 1 ​ (iii) e = 1 = ω 2 l ​ − 0 V − ( − V 1 ​ ) ​ ⇒ V + V 1 ​ = 2 ω l ​ ; 6 M mω l ​ + 6 ω l ​ = 2 ω l ​ ; ( M m ​ + 1 ) = 3 ⇒ M m ​ = 2 ⇒ M = 2 m ​ = 9 k g .

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