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Question

The displacement of a particle in SHM is $$x=10\sin \begin{pmatrix}2t-\dfrac{\pi}{6}\end{pmatrix}m.$$ When its displacement is 6 m, the velocity of the particle (in $$ms^{-1}$$) is


A
8
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B
24
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C
16
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D
10
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E
12
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Solution

The correct option is D 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, $$\sin^2\theta+cos^2\theta=1$$
$$cos(2t-\pi/6)=\sqrt{1-(3/5)^2}=4/5$$
Now, velocity $$v=\dfrac{dx}{dt}=20cos(2t-\pi/6)=20\times (4/5)=16 \, m/s$$

Physics

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