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A particle rotates in a circular path with angular position θ=(5t⁴)/(40)-(t³)/3 (in rad, t in s). Its angular acceleration at t=10 s is

Asked in JEE Main 27th Jan 2nd Shift 2024 · Equations of rotational motion

(1) 100 rad/s²
(2) 120 rad/s²
(3) 130 rad/s²
(4) 150 rad/s²

Answer: (3) 130 rad/s²

Step-by-step solution

θ=(t⁴)/8-(t³)/3, so ω=(dθ)/(dt)=(t³)/2-t² and α=(dω)/(dt)=(3t²)/2-2t.

At t=10: α=(3(100))/2-20=150-20=130 rad/s².

Why the other options are wrong

(1) Comes from dropping the -2t term at t=10.
(2) Comes from a coefficient slip in the first derivative.
(4) Comes from keeping only the (3t²)/2 term and ignoring -2t.

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