Question

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

• A. $1m$
• B. $2m$
• C. $3m$
• D. $4m$

Answer 1

The correct option is A $1m$

Given,

$\overrightarrow{v}=2\hat{i}m{s}^{-1}{v}_x=2,v_y=0$

$\overrightarrow{a}=(2\hat{i}+4\hat{j})m{s}^{-2}{a}_x=2,a_y=4$

Tangential velocity in circular motion give, centripetal acceleration toward center

Centripetal acceleration is normal to the tangential velocity

$a_y=\frac{v_x^2}{\left|r\right|}$

$\left|r\right|=\frac{v_x^2}{a_y}=\frac{2^2}{4}=1m$

Hence, radius of circle is $1m$