For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown in below figure, the projection of OP on the x -axis at time t is (a) x(t) = rcos (ω t - π/6ω) (b) x(t) = rcos (ω t) (c) x(t) = rcos (ω t + π/6) (d) x(t) = rsin (ω t + π/6)

Answer: (c). At t = 0, OP makes 30° = π/6 with the x -axis. P moves anticlockwise, so at time t the angle is ω t + π/6. Projection on x -axis: x(t) = rcos (ω t + π/6). So the answer is (c).

For particle P revolving round the centre O with radius of circular… | JEE Main 2023 (8 Apr, Shift 2)

Q32JEE Main 2023 · 8 APR · SHIFT 2Easy

Periodic Motion & SHM Basics

For particle P revolving round the centre O with radius of circular path $r$ and angular velocity $\omega$ , as shown in below figure, the projection of OP on the $x$ -axis at time $t$ is

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Answer: (c)

At $t = 0$ , OP makes $30^\circ = \frac{\pi}{6}$ with the $x$ -axis.
P moves anticlockwise, so at time $t$ the angle is $\omega t + \frac{\pi}{6}$ .
Projection on $x$ -axis: $x(t) = r\cos\left(\omega t + \frac{\pi}{6}\right)$ .
So the answer is (c).

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