Question

The equation of motion of a particle started at $t=0$, is given by $y=5\sin \left(20t+\frac{\pi }{3}\right)cm$. The least time after which acceleration becomes zero is:

• A. $\frac{\pi }{90}\sec$
• B. $\frac{\pi }{120}\sec$
• C. $\frac{\pi }{60}\sec$
• D. $\frac{\pi }{30}\sec$

Answer 1

Answer: (D)

$\frac{\pi }{30}\sec$

$a={\omega }^{2}x={\omega }^2\left[5\sin \left(20t+\frac{\pi }{3}\right)\right]$

$Fora=0,5\sin \left(20t+\frac{\pi }{3}\right)=0$

$\Rightarrow \sin \left(20t+\frac{\pi }{3}\right)=\sin \left(\pi \right)$

$\Rightarrow 20t=\pi -\frac{\pi }{3}=\frac{2\pi }{3}$

$\Rightarrow t=\frac{\pi }{30}\sec$

Hence,

option $\left(D\right)$ is correct answer.