Question

A stationary will starts rotating about its own axis at uniform angular acceleration 8rad /s ${}^2$. The time taken by it to complete 77 rotations is

• A. 5.5 sec
• B. 7sec
• C. 11 sec
  
• D. 14 sec

Answer 1

The correct option is C 11 sec

Given,

Angular displacement, $\theta =77\times 2\pi =154\pi rad$

Angular acceleration, $\alpha =8rad/s^2$

Apply equation of motion

$\theta ={\omega }_{o}t+\frac{1}{2}\alpha t^2$

$154\pi =0+\frac{1}{2}\times 8\times t^2$

$t=11\sec$

Hence, in $11sec$ it complete $77$ rotation