Question

For a particle in uniform circular motion, the acceleration a at any point P(R, θ) on the circular path of radius R is (when θ is measured from the positive x-axis and v is uniform speed):

• A. \(-\frac{v^2}{R}sinθi+\frac{v^2}{R}cosθj\)
• B. \(-\frac{v^2}{R}cosθi+\frac{v^2}{R}sinθj\)
• C. \(-\frac{v^2}{R}cosθi-\frac{v^2}{R}sinθj\)
• D. \(-\frac{v^2}{R}i-\frac{v^2}{R}j\)

Answer 1

The Correct Option is A

The correct option is (C): \(-\frac{v^2}{R}cosθi-\frac{v^2}{R}sinθj\).

As the particle in uniform circular motion experiences only centripetal acceleration of magnitude ω²R or

\(\frac{V^2}{R}\)

directed towards centre so from diagram.

\(a=\frac{v^2}{R}cosθ(-i)+\frac{v^2}{R}sin(-j)\)