A particle moves in the x-y plane according to rule $\mathrm{x}=\mathrm{asin\omega t}$ and $\mathrm{y}=\mathrm{acos\omega t}$. The particle follows:

1. an elliptical path.

2. a circular path.

3. a parabolic path.

4. a straight line path inclined equally to the x and y-axis.

Subtopic:  Circular Motion |
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The magnitude of a vector $\stackrel{\to }{\mathrm{A}}$ is constant but it is changing its direction continuously. The angle between $\stackrel{\to }{\mathrm{A}}$ and $\frac{\mathrm{d}\stackrel{\to }{\mathrm{A}}}{\mathrm{dt}}$ is :

1. 180°

2. 120°

3. 90°

4. 0°

Subtopic:  Circular Motion |
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What is the value of linear velocity if $\stackrel{\to }{\omega }=3\stackrel{^}{i}-4\stackrel{^}{j}+\stackrel{^}{k}$ and $\stackrel{\to }{r}=5\stackrel{^}{i}-6\stackrel{^}{j}+6\stackrel{^}{k}$

1. $6\stackrel{^}{i}+2\stackrel{^}{j}-3\stackrel{^}{k}$

2. $-18\stackrel{^}{i}-13\stackrel{^}{j}+2\stackrel{^}{k}$

3. $4\stackrel{^}{i}-13\stackrel{^}{j}+6\stackrel{^}{k}$

4. $6\stackrel{^}{i}-2\stackrel{^}{j}+8\stackrel{^}{k}$

Subtopic:  Circular Motion |
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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. θ1

2. θ2

3. 2θ1

4. 2θ2

Subtopic:  Circular Motion |
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A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\mathrm{\pi }$ sec. 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 |
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If the equation for the displacement of a particle moving on a circular path is given by $\left(\theta \right)=2{t}^{3}+0.5$, where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:

Subtopic:  Circular Motion |
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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.

2. 2K

3. K

4.

Subtopic:  Circular Motion |
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Two particles A and B are moving in a uniform circular motion in concentric circles of radii  with speeds  respectively. Their time periods of rotation are the same. The ratio of angular speed of A  to that of B will be:

1. 1: 1

2.

3.

4.

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. and direction along the tangent to the circle.

2. and direction along the radius towards the centre.

3. and direction along the radius towards the centre.

4. and direction along the radius away from the centre.

Subtopic:  Circular Motion |
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The position vector of a particle is . 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 |
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