Question

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

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

Answer 1

Answer: (C)

$314$

Initial speed ${\nu }_i=1200$ $r.p.m=\frac{1200}{60}$ $r.p.s=20$ $r.p.s$

$\therefore$ $w_i=2\pi {\nu }_i=2\pi \times 20=40\pi$ $rad/s$

Final angular velocity $w_f=0$

Using $w_f^2-w_i^2=2\alpha S$

$\therefore$ $0-(40\pi {)}^2=2(-4)S$

$⟹$ $S=200{\pi }^2$ $rad$

Number of revolution $N=\frac{200{\pi }^2}{2\pi }=100\pi =314$