A wheel has a speed of 1200 rev/min and is made to slow down at a rate of `4 rads^(-2)`. The number of revolutions it makes before coming to rest is

Options

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

Answer

(c)

Explanation

From equation of rotational motion,`omega^(2)=omega_(0)^(2)-2theta`
`0=omega_(0)^(2)-2aomega`
`omega_(0)^(2)=2aomega`
implies `theta=(omega_(0)^(2))/(2a)`
implies `omega_(0)=2piN=2pixx1200xx(1)/(60)=40pirad//s`
implies `r=4rad//s^(2)`
because `theta=(40pi)^(2)/(2xx4)=200pi^(2)`
Number of revolutions `=(200pi^(2))/(2pi)=100pi`
`=314.159cong 314`