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

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, θ=θ0+θ1t+θ2t2. It can be deduced that the angular acceleration of the body is? 

1. θ1

2. θ2

3. 2θ1

4. 2θ2

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 θ 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. K2 + K2t2r2

2. 2K

3. K

4. K2 + K2t2

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 r = a sin ωti^ + a cos ωtj^. The velocity of the particle is:

1.  parallel to the position vector.
2.  at 60° 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 \(\mathrm{v}_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?

                                 

1. \( 2 \mathrm{v}_0 \sin \frac{\theta}{2} \) 1. \( \mathrm{v}_0 \sin \frac{\theta}{2} \)
3. \( 2 \mathrm{v}_0 \cos \frac{\theta}{2} \) 4. \( \mathrm{v}_0 \cos \frac{\theta}{2}\)
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. \(\pi^2 \mathrm{~ms}^{-2} \) 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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