A body is hanging from a rigid support by an extensible string of length L. It is struck inelastically by an identical body of mass m with horizontal velocity v =√2gl , the tension in the string increases just after striking by:
Correct answer: C. 2mg
- A. mg
- B. 3mg
- C. 2mg
- D. None of these
Explanation
Initially, the tension in the string is T = mg, which equals the weight of the hanging body. When struck by an identical body inelastically, the system's mass becomes 2m. Conservation of momentum gives us:mv = 2m(v'), thus v' = v/2.Using the inelastic collision principles, the new tension T' is given by T' - 2mg = 2m(v')^2/L. By substituting v' = v/2 and v = √(2gL), we find T' = 3mg.Therefore, the tension increase is T' - T = 3mg - mg = 2mg.Option A is incorrect as it ignores the momentum change. Option B miscalculates the velocity and resultant tension. Option D is incorrect since the calculated increase in tension is indeed 2mg, making Option C the right choice.
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About Collisions
Collisions involve the conservation of linear momentum when bodies interact for a short time. The topic covers impulse, elastic and inelastic collisions, kinetic energy changes, and the coefficient of restitution, with calculations usually based on one dimensional motion. Momentum remains conserved in isolated collisions, but kinetic energy is conserved only in elastic collisions.
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