JEE Main 2022PhysicsMotion In Two DimensionsMediumMCQ

JEE Main 2022 — Motion In Two Dimensions Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

A ball is spun with angular acceleration α=6t2-2t where t is in second and α is in rad s-2. At t=0, the ball has angular velocity of 10 rad s-1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is

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Show full solutionCorrect option: B
Correct answer
Bt42-t33+10t+4

Step-by-step explanation

Given: α=6t2-2t

Using relation α=dωdt=6t2-2t

Integrating the above, 

∫10ωdω=∫0t6t2-2tdt

⇒ω-10=2t3-t2

Now, ω=dθdt=10+2t3-t2

∫4θdθ=∫0t10+2t3-t2dt

Integrating the above relation, 

θ-4=10t+t42-t33

Thus, angular position of the ball is θ=t42-t33+10t+4.

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About this question

This is a previous-year question from JEE Main 2022, covering the Motion In Two Dimensions chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.