Question

A stationary wheel starts rotating about its own axis at a constant angular acceleration. If the wheel completes $50$ rotations in the first $2s$, then the number of rotations made by it in the next $2s$ is:

• A. $75$
• B. $100$
• C. $125$
• D. $150$

Answer 1

Answer: (D)

$150$

${\omega }_i=0$

$t=2x$

$0=50\left(2\pi \right)=100\pi rad$

$\therefore \alpha =\frac{20}{t^2}=\frac{22\pi }{4}=50\pi rad{s}^{-2}$

${}^{\prime }{0}^{\prime }$ in 4 sec $0=\frac{1}{2}a{t}^2=\frac{1}{2}\left(50\pi \right)\left(16\right)$

$400\pi rad$

in the laser 2 sec, $0=400\pi -100\pi =300\pi rad$

$\therefore$ no of rotations = $\frac{0}{2\pi }=\frac{300\pi }{2\pi }=150$