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?

Question

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? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

It can be observed that the component of acceleration perpendicular to velocity is a=4ms- 2 ∴ Radius =(v2/ac)=((2)2/4)=1 mathrm~m

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

It can be observed that the component of acceleration perpendicular to velocity is $a = 4 m s^{- 2}$
$∴$ Radius $= \frac{v ^{2}}{a _{c}} = \frac{( 2 ) ^{2}}{4} = 1 m$

Q. The velocity and acceleration vectors of a particle undergoing circular motion are v→=2i^ms−1 and a→=2i^+4j^​ms−2 respectively at an instant of time. What is the radius (in m ) of the circle?

It can be observed that the component of acceleration perpendicular to velocity is a=4ms−2 ∴ Radius =ac​v2​=4(2)2​=1 m

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

It can be observed that the component of acceleration perpendicular to velocity is $a = 4 m s^{- 2}$
$∴$ Radius $= \frac{v ^{2}}{a _{c}} = \frac{( 2 ) ^{2}}{4} = 1 m$