The position vector of a particle `vec(R )` as a funtion of time is given by:
`vec(R )= 4sin(2pit)hat(i)+4cos(2pit)hat(j)`
Where `R` is in meters, `t` is in seconds and `hat(i)` and `hat(j)` denote until vectors along x-and y- directions, respectively Which one of the following statements is wrong for the motion of particle ?

Options

A. Path of the particle is a circle of radius 4 meter
B. Acceleration vector is along `-vecR`
C. Magnitude of acceleration vector is `(v^(2))/(R)` where v is the velocity of particle
D. Magnitude of the velocity of particle is 8 meter/second

Answer

D

Explanation

`vecR=4sin(2pit)hati+4cos(2pit)hatj`
`x=4sin2pit` . . . (1)
`y=4cos2pit` . . . (2)
(1) `x^(2)+y^(2)=4(sin^(2)2pit+cos^(2)2pit)`
`x^(2)+y^(2)=4^(2)` equation of circle and radius 4m
(2) `veca=(V^(2))/(R)(-hatR)`
(3) `a=(V^(2))/(R)`
(4) `V_(x)=+4(cos2pit)(2pi)`
and `V_(y)=-4(sin2pit)(2pi)`
`V=sqrt(V_(x)^(2)+V_(x)^(2))`
`=sqrt((8pi)^(2)(cos^(2)2pit+sin^(2)2pit))`
`V=8pi`
so `4^(th)` option is incorrect.