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 |
 54%
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, \(\vec{r}=cos \omega t ~\hat{x}+ sin \omega t~ \hat{y},\) 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 |
 77%
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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