Question

# A shell acquires the initial velocity v = 320 m/s, having made n = 2.0 turns inside the barrel whose length is equal to l = 2.0 m. Assuming that the shell moves inside the barrel with a uniform acceleration, find the angular velocity of its axial rotation at the moment when the shell escapes the barrel.

A

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B

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C

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D

Data insufficient

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Solution

## The correct option is C 2010 radsec When the shell comes out if acquires the velocity of 320 m/s. ⇒ u = 0 v = 320 s = 2 m ⇒ v2 = u2 + 2as (320)2 = 2.a.2 ⇒ a=(160)2 V = u + at 320 = (160)2 t t = (180)sec Now in this time the shell has rotated twice. This means each and every point would have made one angular displacement of θ = 4π ω0 = 0 t = 180 θ = ω0t + 12a t2 ⇒4π = 12a(180)2 a = 8π × (80)2 ωt = ω0 + a t ⇒ ωt = 8π × (80)2 × 180 = 640π ω = 2010 radsec

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