Question

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00$\hat{i}$​ m/s and an acceleration of + 12.5$\hat{j}$​ m/s². What are the x and y coordinates of the center of the circular path?

• A. (4, 6)
• B. (4, 2)
• C. (2, 4)
• D. (6, 4)

Answer 1

The correct option is A

(4, 6)

since $a_c$ points in y direction that means centre should be right above it
We know $a_c$=$\frac{v^2}{R}$
$12.5=\frac{(2{)}^2}{R}$
$\Rightarrow R=2$
$\Rightarrow$ The centre is 2 units above the point(4,4)
$\Rightarrow$ Coordinates of centre =(4,6)