A block of mass m is hanging from a light string of length $ℓ$ . A bullet of mass m strikes the hanging mass and gets embedded into it. The value of v such that the tension in string and the speed of combined mass becomes zero simultaneously during the subsequent motion, is:-

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Combined speed after impact = 2 v ​ . Where speed = 0 , radial equation gives T = 2 m g cos θ . T = 0 there requires θ = 9 0 ∘ : the mass must stop exactly at the horizontal level. Energy: 2 1 ​ ( 2 m ) ( 2 v ​ ) 2 = 2 m g ℓ ⇒ v 2 = 8 g ℓ . Answer: (C)

Physics - Center of Mass Question with Solution | TestHub

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