Question

To enable a particle describe a circular path, what should be the angle between its velocity and acceleration?

• A. ${180}^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$
• D. $0^{\circ }$

Answer 1

Answer: (B)

${90}^{\circ }$

For a particle describing a circular path, the components of velocity along horizontal and vertical directions are $v\sin \theta$ and $v\cos \theta$.

For very small $\theta$,

$\sin \theta =\theta$ and $\cos \theta =1$

Thus, the horizontal component changes from zero to $v\theta$.

Hence, acceleration is always directed towards the center of circle along the radius and is directed at any point such that it is perpendicular to the direction of velocity at that point.