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Q. No.A fan starts from rest and reaches a maximum angular speed of \(\dfrac{20 \pi}{3}~\text{rad/s}\) in \(5~\text{s}.\) What is its angular acceleration?
| 1. | \(\dfrac{8 \pi}{3}~\text{rad/s}^2 \) | 2. | \(\dfrac{4 \pi}{3}~\text{rad/s}^2 \) |
| 3. | \(\dfrac{8}{3}~\text{rad/s}^2 \) | 4. | \(\dfrac{4}{3}~\text{rad/s}^2 \) |
Subtopic: Rotational Motion: Kinematics |
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Level 1: 80%+
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A constant torque of \(1000~\text{N-m}\) rotates a wheel of moment of inertia \(200~\text{kg-m}^2\) about an axis passing through its center. Starting from rest, its angular velocity after \(4~\text s\) is:
| 1. | \(20~\text{rad/s}\) | 2. | \(15~\text{rad/s}\) |
| 3. | \(10~\text{rad/s}\) | 4. | \(2~\text{rad/s}\) |
Subtopic: Rotational Motion: Kinematics |
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Level 1: 80%+
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A particle is moving along a circular path with a radius of \(50\) cm and a linear velocity of \(4\) m/s. The angular velocity of the particle is:
| 1. | \(4~\text{rad/s}\) | 2. | \(5~\text{rad/s}\) |
| 3. | \(8~\text{rad/s}\) | 4. | \(10~\text{rad/s}\) |
Subtopic: Rotational Motion: Kinematics |
88%
Level 1: 80%+
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A ball experiences an angular acceleration given by:
\(\alpha=(6 {t}^2-2 {t}),\)
where \(t\) is in seconds.
At \(t=0,\) the ball has an angular velocity of \(10\) rad/s and an angular position of \(4\) rad. Which of the following expressions correctly represents the angular position \(\theta({t})\) of the ball?
\(\alpha=(6 {t}^2-2 {t}),\)
where \(t\) is in seconds.
At \(t=0,\) the ball has an angular velocity of \(10\) rad/s and an angular position of \(4\) rad. Which of the following expressions correctly represents the angular position \(\theta({t})\) of the ball?
| 1. | \( \dfrac{3}{2} t^4-t^2+10 t \) | 2. | \(\dfrac{t^4}{2}-\dfrac{t^3}{3}+10 t+4 \) |
| 3. | \( \dfrac{2 t^4}{3}-\dfrac{t^3}{6}+10 t+12 \) | 4. | \( 2 t^4-\dfrac{t^3}{2}+5 t+4 \) |
Subtopic: Rotational Motion: Kinematics |
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A disc has angular acceleration \(4~\text{rad/s}^2\) and initial angular speed \(2~\text{rad/s}.\) In \(4~\text s,\) the disc has rotated through an angle of:
1. \(14~\text{rad}\)
2. \(24~\text{rad}\)
3. \(40~\text{rad}\)
4. \(56~\text{rad}\)
1. \(14~\text{rad}\)
2. \(24~\text{rad}\)
3. \(40~\text{rad}\)
4. \(56~\text{rad}\)
Subtopic: Rotational Motion: Kinematics |
84%
Level 1: 80%+
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A body rotates about a fixed axis with a constant angular acceleration of \(3 ~\text {rad/s}^2.\) If its angular velocity increases from \(10~ \text{rad/s}\) to \(20~ \text{rad/s},\) what is the angle (in radians) through which it rotates during this interval?
1. \(50\)
2. \(100\)
3. \(150\)
4. \(200\)
1. \(50\)
2. \(100\)
3. \(150\)
4. \(200\)
Subtopic: Rotational Motion: Kinematics |
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A well-greased laboratory centrifuge operates at \(1500~\text{rpm},\) and is later turned off. If it decelerates at \(136~\text{rev/min}^2,\) how long will it take to stop spinning?
1. \(15~\text{min}\)
2. \(11~\text{min}\)
3. \(9~\text{min}\)
4. \(7~\text{min}\)
1. \(15~\text{min}\)
2. \(11~\text{min}\)
3. \(9~\text{min}\)
4. \(7~\text{min}\)
Subtopic: Rotational Motion: Kinematics |
80%
Level 1: 80%+
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A rigid body rotates about a fixed axis with a variable angular speed given by \(\omega=(3-5 t)\) (in rad/s), where \(t\) is in seconds. The total angle rotated by the body before coming to rest is:
| 1. | \(\dfrac{9}{10}~\text{rad}\) | 2. | \(\dfrac{10}{9}~\text{rad}\) |
| 3. | \(2~\text{rad}\) | 4. | \(10~\text{rad}\) |
Subtopic: Rotational Motion: Kinematics |
79%
Level 2: 60%+
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Q. No.
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