The position vector of a particle $$\vec{R }$$ as a function of time $$t$$ is given by:
$$\vec{{R}}=4 \sin (2 \pi {t}) \hat{i}+4 \cos (2 \pi {t}) \hat{j},$$
where $$R$$ is in metres, $$t$$ is in seconds and $${\hat{i},\hat{j}}$$ denotes unit vectors along $${x}$$ and $${y}\text-$$directions, respectively. Which one of the following statements is wrong for the motion of the particle?
 1 Acceleration is along $$(\text{-}\vec R )$$. 2 Magnitude of the acceleration vector is $$\frac{v^2}{R}$$, where $$v$$ is the velocity of the particle. 3 Magnitude of the velocity of the particle is $$8$$ m/s. 4 Path of the particle is a circle of radius $$4$$ m.
Subtopic: Â Circular Motion |
Â 61%
From NCERT
NEET - 2015
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A particle moves in a circle of radius $$5$$ cm with constant speed and time period $$0.2\pi$$ s. The acceleration of the particle is:

 1 $$25$$ m/s2 2 $$36$$ m/s2 3 $$5$$ m/s2 4 $$15$$ m/s2
Subtopic: Â Circular Motion |
Â 80%
From NCERT
AIPMT - 2011
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A particle moves in the $$(x\text-y)$$ plane according to the rule $$x = a \sin (\omega t)$$ and $$y = a \cos (\omega t)$$. The particle follows:

 1 a circular path. 2 a parabolic path. 3 a straight line path inclined equally to x and y-axes. 4 an elliptical path.
Subtopic: Â Circular Motion |
Â 77%
From NCERT
AIPMT - 2010
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