Motion in a Plane - Result Question 43
46. The position vector of a particle $\vec{R}$ as a function of time is given by:
$\vec{R}=4 \sin (2 \pi t) \hat{i}+4 \cos (2 \pi t) \hat{j}$
Where $R$ is in meter, $t$ in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along $x$-and $y$-directions, respectively.
Which one of the following statements is wrong for the motion of particle?
[2015 RS]
(a) Magnitude of acceleration vector is $\frac{v^{2}}{R}$, where $v$ is the velocity of particle
(b) Magnitude of the velocity of particle is 8 meter/second
(c) path of the particle is a circle of radius 4 meter.
(d) Acceleration vector is along $\vec{R}$
Show Answer
Answer:
Correct Answer: 46. (b)
Solution:
- (b) Here, $x=4 \sin (2 \pi t)$
$ \begin{equation*} y=4 \cos (2 \pi t) \tag{i} \end{equation*} $
Squaring and adding equation (i) and (ii) $x^{2}+y^{2}=4^{2} \Rightarrow R=4$
Motion of the particle is circular motion, acceleration vector is along $-\vec{R}$ and its magnitude $=\frac{V^{2}}{R}$
Velocity of particle, $V=\omega R=(2 \pi)(4)=8 \pi$
