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)

1 m

Answer 2

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