The angle turned by a body undergoing circular motion depends on the time as given by the equation, $$\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}$$. It can be deduced that the angular acceleration of the body is?
1. $$\theta_1$$
2. $$\theta_2$$
3. $$2\theta_1$$
4. $$2\theta_2$$

Subtopic:  Circular Motion |
84%
From NCERT
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If the equation for the displacement of a particle moving on a circular path is given by $$\theta = 2t^3 + 0.5$$ where $$\theta$$ is in radians and $$t$$ in seconds, then the angular velocity of the particle after $$2$$ sec from its start is:
1. $$8$$ rad/sec
2. $$12$$ rad/sec
3. $$24$$ rad/sec
4. $$36$$ rad/sec

Subtopic:  Circular Motion |
81%
From NCERT
AIIMS - 1998
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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 car moves on a circular path such that its speed is given by $$v= Kt$$, where $$K$$ = constant and $$t$$ is time. Also given: radius of the circular path is $$r$$. The net acceleration of the car at time $$t$$ will be:
1. $$\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}$$
2. $$2K$$
3. $$K$$
4. $$\sqrt{K^{2} + K^{2} t^{2}}$$

Subtopic:  Circular Motion |
80%
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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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The position vector of a particle is $$\overrightarrow{r}= a \sin\omega t\hat i + a\cos \omega t\hat j$$. The velocity of the particle is:

 1 parallel to the position vector. 2 at $$60^{\circ}$$ with position vector. 3 parallel to the acceleration vector. 4 perpendicular to the position vector.
Subtopic:  Circular Motion |
79%
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A particle is moving along a circle of radius $$R$$ with constant speed $$v_0$$. What is the magnitude of change in velocity when the particle goes from point $$A$$ to $$B$$ as shown?

 1 $$2{v}_0 \sin \frac{\theta}{2}$$ 2 $$v_0 \sin \frac{\theta}{2}$$ 3 $$2 v_0 \cos \frac{\theta}{2}$$ 4 $$v_0 \cos \frac{\theta}{2}$$
Subtopic:  Circular Motion |
78%
From NCERT
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If a particle is moving in a circular orbit with constant speed, then:

 1 its velocity is variable. 2 its acceleration is variable. 3 its angular momentum is constant. 4 All of the above

Subtopic:  Circular Motion |
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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 |
77%
From NCERT
AIPMT - 2005
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In a uniform circular motion, if the speed of the particle is $$2$$ m/s and radius of the circle is $$2$$ m, then the values of centripetal and tangential acceleration are, respectively:
1. $$2~\text{m/s}^2,~2~\text{m/s}^2$$

2. $$2~\text{m/s}^2,~1~\text{m/s}^2$$
3. $$0,~2~\text{m/s}^2$$
4. $$2~\text{m/s}^2,~0$$

Subtopic:  Circular Motion |
75%
From NCERT
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