Question

A wheel has a speed of $1200$ revolutions per minute and is made to slow down at a rate of $4radians/s^2$. The number of revolutions it makes before coming to rest is:

• A. $143$
• B. $272$
• C. $314$
• D. $722$

Answer 1

The correct option is C $314$

Given angular retardation$=4rad/s^2$
Angular velocity$=1200\times \frac{2\pi }{60}rad/s$
$=40\pi rad/s$
$\therefore {\omega }^2=2\alpha \theta$
$\Rightarrow \theta =\frac{{\omega }^2}{2\alpha }=\frac{40\pi \times 40\pi }{2\times 4}=200{\pi }^2$
$Numberofrevolutions=\frac{\theta }{2\pi }=100\pi =314$