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Q. No.

Which of the following is the angle between velocity and acceleration of a body in uniform circular motion?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)

Subtopic:  Circular Motion |
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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 |
 88%
Level 1: 80%+
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Two particles are moving along the same circular path. If the ratio of their centripetal accelerations is \(3:4,\) then the ratio of their tangential velocities is:
1. \(2:\sqrt3\) 2. \(\sqrt3:2 \)
3. \(\sqrt3:1\) 4. \(1:\sqrt{3}\)
Subtopic:  Circular Motion |
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Level 1: 80%+
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The angle turned by a body undergoing circular motion depends on time as θ=θ0+θ1t+θ2t2. Then 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 0.2π 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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A particle moving in a uniform circular motion of radius \(1\) m has velocity \(3 \hat j ~\text {m/s}\) at point \(B.\) What are the velocity \((\vec{v})\)and acceleration \((\vec{a})\) at diametrically opposite point \(A?\) 
1. \( \vec{v}_A=3 \hat{j}~\text{m/s} ;~\vec{a}_A=-9 \hat{i}~\text{m/s}^2\)
2. \( \vec{v}_A=-3 \hat{j}~\text{m/s};~\vec{a}_A=9 \hat{i}~\text{m/s}^2\)
3. \(\vec{v}_A=-3 \hat{i}~~\text{m/s};\vec{a}_A=9 \hat{j}~\text{m/s}^2\)
4. \(\vec{v}_A=3 \hat{i}~\text{m/s} ;~\vec{a}_A=9 \hat{j}~\text{m/s}^2 \)
Subtopic:  Circular Motion |
 82%
Level 1: 80%+
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A particle moves along a circular path of radius \(9~\text{m}\) and completes \(120\) revolutions in \(3\) minutes. What is the centripetal acceleration of the particle?
1. \(8 \pi^2 ~\text{m/s}^2\)
2. \(16 \pi^2~\text{m/s}^2\)
3. \(32 \pi^2~\text{m/s}^2\)
4. \(16 \pi ~\text{m/s}^2\)

Subtopic:  Circular Motion |
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Level 1: 80%+
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A particle moves in a circle of radius \(1.0\) cm at a speed given by, \(v=2.0t\) where \(v\) is in cm/s and \(t\) in seconds. Find the magnitude of the acceleration at \(t=1~\text{s}\).
1. \(\sqrt{20}~\text{cm/s}^2\) 2. \(\sqrt{10}~\text{cm/s}^2\)
3. \(20~\text{cm/s}^2\) 4. \(10~\text{cm/s}^2\)
Subtopic:  Circular Motion |
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A body of mass \(m\) is moving in a horizontal circle of radius \(R\) with a frequency \(\nu.\) Which of the following represents the magnitude of the centripetal acceleration acting on the body?
1. \(4m\pi \nu^2R \) 2. \(4\pi^2 \nu R \)
3. \(4\pi^2 \nu^2R \) 4. \(4\pi^2 \nu^2R^2 \)
Subtopic:  Circular Motion |
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A body moves with a constant speed along a curved path in a plane, as shown in the figure. Which of the following options correctly represents the direction of its acceleration vector at the given instant?
1. \(\overrightarrow{a}_1\) 2. \(\overrightarrow{a}_2\)
3. \(\overrightarrow{a}_3\) 4. none of the above
Subtopic:  Circular Motion |
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