1. Tardigrade
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  4. The velocity and acceleration vectors of a particle undergoing circular motion are overset arrow v=2 hat texti m s- 1 and overset arrow a=2 hat texti+4 hat textj m s- 2 respectively at an instant of time. What is the radius (in textm ) of the circle?

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Q. The velocity and acceleration vectors of a particle undergoing circular motion are $\overset{ \rightarrow }{v}=2\hat{\text{i}} \, m \, s^{- 1}$ and $\overset{ \rightarrow }{a}=2\hat{\text{i}}+4\hat{\text{j}} \, m \, s^{- 2}$ respectively at an instant of time. What is the radius (in $\text{m}$ ) of the circle?

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

It can be observed that the component of acceleration perpendicular to velocity is $a=4ms^{- 2}$
$\therefore \quad$ Radius $=\frac{v^2}{a_c}=\frac{(2)^2}{4}=1 \mathrm{~m}$