Question

A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\overrightarrow{a} = (4\widehat{i} + 3\widehat{j})$ m/s² and $\overrightarrow{p} = (8\widehat{i} - 6\widehat{j})$ kg-m/s. The motion of the particle is

• A. Uniform circular motion
• B. Accelerated circular motion
• C. Decelerated circular motion
• D. We cannot say anything with $\overrightarrow{a}$ and $\overrightarrow{p}$only

Answer 1

Answer: (B)

Accelerated circular motion

Answer 2

Angle between $\overrightarrow{a}$and $\overrightarrow{p}$ is :

q = cos^–1 $\frac{\overrightarrow{a}.\overrightarrow{p}}{|\overrightarrow{a}||\overrightarrow{p}|}$

= cos^‑1 $\left\{ \frac{32 - 18}{\sqrt{(16 + 9)\sqrt{(64 + 36)}}} \right\}$

= cos^–1 $\left( \frac{14}{50} \right)$

q = 73.73⁰

Since 0⁰ < 90⁰, the motion is an acceleration one.