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(A) In circular motion,the acceleration vector $\overrightarrow{a}$ can be resolved into two components: the centripetal acceleration $\overrightarrow

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(A) In circular motion,the acceleration vector $\overrightarrow{a}$ can be resolved into two components: the centripetal acceleration $\overrightarrow{a}_c$ (perpendicular to velocity) and the tangential acceleration $\overrightarrow{a}_t$ (parallel to velocity).Given $\overrightarrow{v} = 2 \hat{i} 	ext{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} 	ext{ m/s}^2$.The component of acceleration perpendicular to the velocity is the centripetal acceleration,$a_c$.Since $\overrightarrow{v}$ is along the $\hat{i}$ direction,the component of $\overrightarrow{a}$ perpendicular to $\overrightarrow{v}$ is the $\hat{j}$ component,which is $a_c = 4 	ext{ m/s}^2$.The formula for centripetal acceleration is $a_c = \frac{v^2}{R}$,where $R$ is the radius of the circle.Rearranging for $R$,we get $R = \frac{v^2}{a_c}$.Substituting the values: $R = \frac{(2)^2}{4} = \frac{4}{4} = 1 	ext{ m}$.

The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

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