Question

Two particles are moving in uniform circular motion in opposite direction with same angular velocity. Radius of the circle is $R$. Their resultant motion is equivalent to :

• A. angular SHM of angular frequency $2\omega$
• B. linear SHM of angular frequency $2\omega$
• C. linear SHM of amplitude $2R$
• D. angular SHM of amplitude $2$ radians

Answer 1

The correct option is C linear SHM of amplitude $2R$

Position vector of first particle can be taken as $\overrightarrow{r_1}=R(\cos \omega t\hat{i}+\sin \omega t\hat{j})$
Position vector of second particle can be taken as $\overrightarrow{r_2}=R(\cos \omega t\hat{i}-\sin \omega t\hat{j})$
Resultant of both the vectors is $2R\sin \omega t\hat{i}$, which shows a linear SHM of amplitude $2R$