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. (a) Path of particle is a circle of radius `4` metre
B. (b) Acceleration vector is along ` vec -R`
C. (c ) Magniude fo acceleration vector is ` v^2//R`,
D. (d)` Magniued to the velocity of particle is `8` metre //second

Answer

D

Explanation

Here, ` x = 4 sin 2 pi t ` and ` y = 4 cos 2 pi t`
squaring and adding we have
` x^2 +y^2= 4^2 (sin^2 2 pi t+ cos^2 2 pi t ) = 4^2`
It is an equation of a circle of radius `4` metre.
For circular motion, the accelerated is along ` - vec R` and magnitude of acceleration is ` v^2 // R`.
Given ` vec R= 4 sin 9 2 pi t ) hat i + 4 cos ( 2 pi t) hat j` ltbRgt velocity , ` vec v = (d vec R)/(dt)`
`= 4 xx 2 pi cos (2 pi t) hat i+ 4 xx pi sin (2 pi t) hat j`
`= 8 pi [ cos ( 2 pi t) hat i+ sin ( 2 pi t) hat j]`
Magnitude of velocity ,` | vec v| = 8s pi`
Thus, option (d) wrong.