What is the value of linear velocity if \(\overrightarrow{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overrightarrow{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\) :

1. \(6 \hat{i}+2 \hat{j}-3 \hat{k} \)           
2. \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \)
3. \(4 \hat{i}-13 \hat{j}+6 \hat{k}\)
4. \(6 \hat{i}-2 \hat{j}+8 \hat{k}\)
Subtopic:  Circular Motion |
 85%
From NCERT
PMT - 2000
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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%
From NCERT
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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%
From NCERT
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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 |
 77%
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 |
 78%
From NCERT
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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 |
 76%
From NCERT
AIPMT - 2005
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