AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A flywheel with the initial angular velocity 12 rad / s decelerates due to the forces whose moment relative to the axis is proportional to the square root of its angular velocity. Find the mean angular velocity of the flywheel average over the total deceleration time in rads^-1

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is 4.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

According to the question,

Let $Iα = - k \sqrt{ω}$
$\begin{array}{l} I \frac{dω}{dt} = - k \sqrt{ω} \end{array}$

$I \frac{d ω}{\sqrt{ω}} = - kdt$

$Integrating, \sqrt{ω} = - \frac{kt}{2 I} + \sqrt{ω_{0}}$

$or, ω = \frac{k^{2} t^{2}}{4 I^{2}} - \frac{\sqrt{ω_{0} kt}}{I} + ω_{0}$

$(Noting that at t = 0, ω = ω_{0})$

$Let the flywheel stops at t = t_{0} then from equation (1), t_{0} = \frac{2 I \sqrt{ω_{0}}}{k}$

$<ω> = \frac{\int_{0}^{t_{0}} d d ωdt}{\int_{0}^{t_{0}} d dt} = \frac{ω_{0}}{3} = 4 rad / s$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!