Question

The velocity and acceleration vectors of a particle undergoing circular motion are $\vec{v}=2\hat{m}/s$ and $\vec{a}=2\hat{1}+4\hat{j}m/s^2$ respectively at an instant of time. The radius of the circle is

• A. 1 m
• B. 2 m
• C. 3 m
• D. 4 m

Answer 1

Answer: (A)

Given,
$\vec{v}=2\hat{i}m{s}^{-1}{v}_x=2,v_y=0$
$\vec{a}=(2\hat{i}+4\hat{j})m{s}^{-2}{a}_x=2,a_y=4$
Tangential velocity in circular motion give, centripetal acceleration toward center Centripetal acceleration is normal to the tangential velocity
$a_y=\frac{v_x^2}{|r|}$
$|r|=\frac{v_x^2}{a_y}=\frac{2^2}{4}=1m$
Hence, radius of circle is $1m$