Two small bodies of masses ‘m’ and ‘2m’ are placed in a fixed smooth horizontal circular hollow tube of mean radius 'r' as shown. The mass ‘m’ is moving with speed ‘u’ and the mass ‘2m’ is stationary. After their first collision, the time elapsed for next collision is: (coefficient of restitution e = 1/2)

Engineering

Physics

Collision

Question

$\frac{4 πr}{u}$

$\frac{3 πr}{u}$

$\frac{2 πr}{u}$

$\frac{12 πr}{u}$

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If just after collision, relative velocity = v, then v/u = 1/2
∴ ω_rel = v/r = u/(2r)
∴ time between 1^st and 2^nd collision, t = 2π/ω_rel = 4πr/u