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Question:

For a particle in uniform circular motion, the acceleration →a at a point P(R, θ) on the circle of radius R is (here 'v' is the speed of the particle and θ is measured from the x-axis)

−v²Rcosθ^i+v²Rsinθ^j

−v²Rcosθ^i−v²Rsinθ^j

−v²Rsinθ^i+v²Rcosθ^j

v²R^i+v²R^j

Solution:

For a particle in uniform circular motion, →a=v²/R towards centre of circle
∴ →a=v²/R(−cosθ^i−sinθ^j)
or →a=−v²Rcosθ^i−v²Rsinθ^j