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A ball is spun with angular acceleration α=6t²-2t (in rad/s²). If it starts from rest, its angular velocity at t=2 s is

Asked in JEE Main 15th April 1st Shift 2023 · Equations of rotational motion

(1) 8 rad/s
(2) 12 rad/s
(3) 16 rad/s
(4) 20 rad/s

Answer: (2) 12 rad/s

Step-by-step solution

ω=∫₀^t(6t²-2t) dt=2t³-t².

At t=2: ω=2(8)-4=12 rad/s.

Why the other options are wrong

(1) Comes from integrating 6t² only and dropping -2t.
(3) Comes from forgetting to subtract the t² term at t=2.
(4) Comes from mis-integrating 6t² as 6t³.

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