Question

Assertion: Time taken by a particle executing $\text{SHM}$ of amplitude A to move from $x=A$ to $x=\frac{\sqrt{3}A}{2}$ is same as the time taken by the particle to move from $x=\frac{\sqrt{3}A}{2}$ to $x=\frac{A}{2}$.
Reason: Corresponding angles rotated in the reference circle are same in the given time intervals.

• A. If both assertion and reason are true and the reason is correct explanation of the assertion.
• B. If both assertion and reason are true but reason is not the correct explantion of assertion.
• C. If assertion is true but the reason is false.
• D. If assertion is false but the reason is true.

Answer 1

The correct option is A If both assertion and reason are true and the reason is correct explanation of the assertion.


Time taken by a particle to move from $x=A$ to $x=\frac{\sqrt{3}A}{2}$
$t_1=\frac{\theta }{w}=\frac{\frac{\pi }{6}}{\frac{2\pi }{T}}=\frac{T}{12}$
Time taken by a praticle to move from $x=\frac{\sqrt{3}A}{2}$ to $\frac{A}{2}$
$t_2=\frac{\frac{\pi }{6}}{\frac{2\pi }{T}}=\frac{T}{12}$
$\therefore t_1=t_2$ since, the corresponding angles rotated in reference circle are also same.