Q. No.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 |
52%
From NCERT
NEET - 2016
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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. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the tangent to the circle. |
| 2. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the radius towards the centre. |
| 3. | \(\frac{\pi^2}{4}~\text{ms}^{-2} \) and direction along the radius towards the centre. |
| 4. | \(\pi^2~\text{ms}^{-2} \) and direction along the radius away from the centre. |
Subtopic: Circular Motion |
78%
From NCERT
AIPMT - 2005
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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. | The velocity and acceleration both are parallel to \(\vec{r }.\) |
| 2. | The velocity is perpendicular to \(\vec{r }\) and acceleration is directed towards to origin. |
| 3. | The velocity is parallel to \(\vec{r }\) and acceleration is directed away from the origin. |
| 4. | The velocity and acceleration both are perpendicular to \(\vec{r}.\) |
Subtopic: Circular Motion |
78%
From NCERT
NEET - 2016
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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 |
64%
From NCERT
NEET - 2023
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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 |
62%
From NCERT
NEET - 2016
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A car is moving at a speed of \(40\) m/s on a circular track of radius \(400\) m. This speed is increasing at the rate of \(3\) m/s2. The acceleration of the car is:
1. \(4\) m/s2
2. \(7\) m/s2
3. \(5\) m/s2
4. \(3\) m/s2
Subtopic: Circular Motion |
76%
From NCERT
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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?
\(\vec{{R}}=4 \sin (2 \pi {t}) \hat{i}+4 \cos (2 \pi {t}) \hat{j},\)
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: Circular Motion |
62%
From NCERT
NEET - 2015
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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 |
80%
From NCERT
NEET - 2019
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A car of mass \(m\) moves in a horizontal circular path of radius \(r\) metre. At an instant, its speed is \(v\) m/s and is increasing at a rate of \(a\) m/s2. Then the acceleration of the car is:
| 1. | \(\dfrac{{v}^{2}}{r}\) | 2. | \(a\) |
| 3. | \(\sqrt{{a}^{2}{+}{\left({\dfrac{{v}^{2}}{r}}\right)}^{2}}\) | 4. | \(\sqrt{a+\dfrac{v^{2}}{r}}\) |
Subtopic: Circular Motion |
89%
From NCERT
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A particle of a mass \(m\) is moving in a circle of the radius \(r\) with uniform speed \(v.\) Choose the correct option:
| 1. | radial acceleration \(a_{r}=0;\) tangential acceleration \(a_{t}\neq 0.\) |
| 2. | radial acceleration \(a_{r}=0;\) tangential acceleration \(a_{t}=0.\) |
| 3. | radial acceleration \(a_{r}\neq 0;\) tangential acceleration \(a_{t}\neq 0.\) |
| 4. | radial acceleration \(a_{r}\neq 0;\) tangential acceleration \(a_{t}=0\) |
Subtopic: Circular Motion |
74%
From NCERT
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