KCET 2025 Physics Paper

To determine the acceleration of a particle in uniform circular motion, we start with the equation of the circle:$(x-2)^2+y^2=25$This equation represents a circle with its center at $(2,0)$ and a radius $r$ of 5 meters, derived from:$r^2=25 \Rightarrow r=5$ In uniform circular motion, the centripetal acceleration $a_c$ is given by the formula:$a_c=\;\frac{v^2}{r}$Substituting the given speed $v=2\ \mathrm{m}/\mathrm{s}$ and the radius $r=5\ \mathrm{m}$ :$a_c=\;\frac{2^2}{5}=\;\frac{4}{5}=0.8\ \mathrm{m}/\mathrm{s}^2$ When the particle is at the lowest $y$-coordinate, it is at the point $(2,-5)$, assuming downward is along the negative $y$-axis. At this point, the acceleration vector, which is directed towards the center of the circle, points horizontally to the right towards the center $(2,0)$. Therefore, the acceleration is entirely in the $\hat{i}$ direction:$\vec{a_e}=0.8\ \hat{i}\ \mathrm{m}/\mathrm{s}^2$