Rotational Motion

JEE Main level, single correct, medium

160 of 280

Question 160 of 280

A fly wheel is accelerated uniformly from rest and rotates through 5rad5rad in the first second. The angle rotated by the fly wheel in the next second, will be :

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Answer: (B) 15rad15rad

Here the angular acceleration is constant, so we have,
θ=ωt+12αt2\theta =\omega t+\dfrac{1}{2}\alpha {t}^{2}.
When flywheel is rotated from rest in the first second, then θ1=12α(1)2=5rad{\theta }_{1}=\dfrac{1}{2}\alpha {\left(1\right)}^{2}=5rad
⇒α=10rads−2\Rightarrow \alpha =10rad{s}^{-2}
The angle turned by flywheel in the next second is θ2=12α(2)2=12(10)(4)=20rads−2{\theta }_{2}=\dfrac{1}{2}\alpha {\left(2\right)}^{2}=\dfrac{1}{2}\left(10\right)\left(4\right)=20rad{s}^{-2}
Thus, the angle turned during next second is θ=20−5=15rad\theta =20-5=15rad

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