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

1. 1 m
2. 2 m
3. 3 m
4. 4 m

Correct answer: 1 m

Solution

Here velocity is along $\hat i$, so the tangential acceleration is the $\hat i$ component, and the radial acceleration is the perpendicular $\hat j$ component, which has magnitude $4\,\text{m/s}^2$. Using $a_r=v^2/r$, we get $4=2^2/r$, so $r=1\,\text{m}$.

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