Question

Assertion :A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, will perform SHM only if the two SHM's are in the same direction. Reason: A particle, simultaneously subjected to two simple harmonic motions of same frequency and same amplitude, perpendicular to each other the particle will be in uniform circular motion.

• 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. Assertion is incorrect and Reason is incorrect

Answer 1

The correct option is D Assertion is incorrect and Reason is incorrect

The first statement is wrong because two SHM's can be superimposed at an angle instead of having the same amplitude and frequency. But, if it is superimposed in opposite direction its resultant becomes zero.

The second statement is a true statement because for perpendicular superimposition.

Consider a wave,

$x=A_{0}cos{\omega }_{0}t$

then, $y=Acos({\omega }_{0}t+\frac{\pi }{2})$

On superimpositon,

$x^2+y^2=A^2{cos}^2{\omega }_{0}t+A^2{sin}^2{\omega }_{0}t$

$x^2+y^2=A^2$

This proves that the particle will perform circular motion.