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Q.

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

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a

3 m

b

4 m

c

2 m

d

1 m

answer is A.

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Detailed Solution

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$4 \hat{j}$ Component is perpendicular to velocity. So, it is radial (or normal) acceleration

$\begin{array}{l} ∴ a_{n} = \frac{v^{2}}{R} \\ o r R = \frac{v^{2}}{a_{n}} = \frac{{(2)}^{2}}{4} = 1 m \end{array}$

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The velocity and acceleration vectors of a particle undergoing circular motion are v→=2i^ m/s and a→=2i^+4j^ m/s2 respectively at some instant of time. The radius of the circle is