A particle is executing uniform circular motion with velocity $$\vec v$$ and acceleration $$\vec a.$$ Which of the following is true?
 1 $$\vec v$$ is a constant; $$\vec a$$ is not a constant 2 $$\vec v$$ is not a constant;  $$\vec a$$ is not a constant 3 $$\vec v$$ is a constant;   $$\vec a$$ is a constant 4 $$\vec v$$ is not a constant;    $$\vec a$$ is a constant
Subtopic:  Circular Motion |
53%
From NCERT
NEET - 2023
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii $$r_A$$ and $$r_B$$ with speeds $$v_A$$ and $$v_B$$ respectively. Their time periods of rotation are the same. The ratio of the angular speed of $$A$$  to that of $$B$$ will be:

 1 $$1: 1$$ 2 $$r_A: r_B$$ 3 $$v_A: v_B$$ 4 $$r_B: r_A$$
Subtopic:  Circular Motion |
79%
From NCERT
NEET - 2019
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In the given figure, $$a=15$$ m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $$R=2.5$$ m at a given instant of time. The speed of the particle is:

1. $$4.5$$ m/s
2. $$5.0$$ m/s
3. $$5.7$$ m/s
4. $$6.2$$ m/s

Subtopic:  Circular Motion |
61%
From NCERT
NEET - 2016
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A particle moves so that its position vector is given by, $$\vec{r}=\mathrm{cos} \omega t ~\hat{x}+ \mathrm{sin} \omega t~ \hat{y},$$ where $$\omega$$ is a constant. Which of the following is true?

 1 velocity and acceleration both are parallel to $$\vec{r}.$$ 2 velocity is perpendicular to $$\vec{r}$$ and acceleration is directed towards to origin. 3 velocity is parallel to $$\vec{r}$$ and acceleration is directed away from the origin. 4 velocity and acceleration both are perpendicular to $$\vec{r}.$$
Subtopic:  Circular Motion |
78%
From NCERT
NEET - 2016
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A particle of mass $$10$$ g moves along a circle of radius $$6.4$$ cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to $$8 \times 10^{-4}$$ J by the end of the second revolution after the beginning of the motion?
 1 $$0.15$$ m/s2 2 $$0.18$$ m/s2 3 $$0.2$$ m/s2 4 ​​​​​​$$0.1$$ m/s2
Subtopic:  Circular Motion |
53%
From NCERT
NEET - 2016
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The position vector of a particle $$\vec{R}$$ as a function of time $$t$$ is given by;
$$\overrightarrow{\mathrm{R}}=4 \sin (2 \pi \mathrm{t}) \hat{\mathrm{i}}+4 \cos (2 \pi \mathrm{t}) \hat{\mathrm{j}}$$
Where $$R$$ is in meters, $$t$$ is in seconds and $$\mathrm{\hat{i},\hat{j}}$$ denotes unit vectors along $$\mathrm{x}$$ and $$\mathrm{y}$$-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

 1 acceleration is along $$-\overrightarrow{R}$$. 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:  Circular Motion |
60%
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:  Circular Motion |
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:  Circular Motion |
76%
From NCERT
AIPMT - 2010
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A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

 1 $$\pi^2 \mathrm{~ms}^{-2}$$ and direction along the tangent to the circle. 2 $$\pi^2 \mathrm{~ms}^{-2}$$  and direction along the radius towards the centre. 3 $$\frac{\pi^2}{4} \mathrm{~ms}^{-2}$$ and direction along the radius towards the centre. 4 $$\pi^2 \mathrm{~ms}^{-2}$$ and direction along the radius away from the centre.

Subtopic:  Circular Motion |
76%
From NCERT
AIPMT - 2005
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A particle moves along a circle of radius $${{20}\over{\pi}} m$$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. 40 ms–2

2. 640π ms–2

3. 160π ms–2

4. 40π ms–2

Subtopic:  Circular Motion |
56%
From NCERT
AIPMT - 2003
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