The correct Solution is (4)
$
\begin{array}{l}
\mathrm{x}=45 \mathrm{~m} 2 \pi \mathrm{t} \\
\mathrm{y}=4 \cos (2 \pi \mathrm{t})
\end{array}
$
On Squaring and adding.
$\Rightarrow$ Circular motion
$
V=\omega=(2 \pi)(4)=8 \pi
$
The position vector of a particle $\overrightarrow{\mathrm{R}}$ as a function of time is given by: $ \overline{\mathrm{R}}=4 \sin (2 \pi t) \hat{1}+4 \cos (2 \pi t)] $Where $\mathrm{R}$ is in meters, $\mathrm{t}$ is in seconds and Î and j denote unit vectors along $\mathrm{x}$ – and $\mathrm{y}$-directions, respectively. Which one of the following statements is wrong for the motion of particle? (1) Patch of the particle is a circle of radius 4 meter (2) Acceleration vector is along $-\overline{\mathrm{R}}$ (3) Magnitude of acceleration vector is $\frac{v^{2}}{R}$, where $v$ is the velocity of particle (4) Magnitude of the velocity of particle is 8 meter/second,
The position vector of a particle $\overrightarrow{\mathrm{R}}$ as a function of time is given by: $ \overline{\mathrm{R}}=4 \sin (2 \pi t) \hat{1}+4 \cos (2 \pi t)] $Where $\mathrm{R}$ is in meters, $\mathrm{t}$ is in seconds and Î and j denote unit vectors along $\mathrm{x}$ – and $\mathrm{y}$-directions, respectively. Which one of the following statements is wrong for the motion of particle? (1) Patch of the particle is a circle of radius 4 meter (2) Acceleration vector is along $-\overline{\mathrm{R}}$ (3) Magnitude of acceleration vector is $\frac{v^{2}}{R}$, where $v$ is the velocity of particle (4) Magnitude of the velocity of particle is 8 meter/second,