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# The Displacement of a Particle is Given by → R = a ( → I Cos ω T + → J Sin ω T ) . the Motion of the Particle is - Physics

MCQ

The displacement of a particle is given by $\overrightarrow{r} = A\left( \overrightarrow{i} \cos\omega t + \overrightarrow{j} \sin\omega t \right) .$ The motion of the particle is

#### Options

• simple harmonic

• on a straight line

• on a circle

• with constant acceleration

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#### Solution

on a circle

We know,

$\frac{\text {d}^2}{\text {dt}^2} \overrightarrow{r} = - \omega^2 \overrightarrow{r}$

But there is a phase difference of 90o between the x and y components because of which the particle executes a circular motion and hence, the projection of the particle on the diameter executes a simple harmonic motion.

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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 12 Simple Harmonics Motion
MCQ | Q 8 | Page 250
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