Question

The displacement of a particle in SHM is $x=10\sin \left(\begin{array}{c}2t-\frac{\pi }{6}\end{array}\right)m.$ When its displacement is 6 m, the velocity of the particle (in $m{s}^{-1}$) is

• A. 8
• B. 24
• C. 16
• D. 10
• E. 12

Answer 1

Answer: (C)

16

Given, $x=10\sin (2t-\pi /6)$

Putting $x=6\Rightarrow 6=10\sin (2t-\pi /6)$

So, $\sin (2t-\pi /6)=3/5$

Using formula, ${\sin }^2\theta +co{s}^2\theta =1$

$cos(2t-\pi /6)=\sqrt{1-(3/5{)}^2}=4/5$

Now, velocity $v=\frac{dx}{dt}=20cos(2t-\pi /6)=20\times \left(4/5\right)=16m/s$