Question

Assertion :A particle is under SHM along the x-axis. Its mean position is x=2, amplitude is A=2 and angular frequency $\omega$. At t=0, particle is at origin, then x-co ordinate versus time equation of the particle will be $x=-2\cos \omega t+2$ Reason: At t=0 particle is at rest.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

The displacement equation of the particle executing $SHM$ about $x=2$ should be in the form as- $x_1=Asin(wt+\varphi )$ where $A$ is the amplitude of oscillation, $A=2$

Thus x co-ordinate versus time equation of the particle $x=2+2sin(wt+\varphi )$ ...........(1)

As the particle is at origin i.e $x=0$ at the instant $t=0$,

$\therefore Att=0,0=2+2sin\left(\varphi \right)⟹\varphi =-\frac{\pi }{2}$

Thus equation (1) $⟹x=2-2coswt$

Now velocity equation is given by $v=2wsinwt$

$\therefore Att=0,⟹v=0$

Thus position of the particle is responsible for the outcome of displacement equation, not the velocity.

Hence both the Assertion and the Reason are correct but Reason is not the correct explanation of the Assertion.