Q. No.Given below are two statements:
| Assertion (A): | \(\vec{v}=\vec{\omega} \times \vec{r}\). (the symbols have their usual meanings) |
| Reason (R): | The cross product of vectors is not commutative. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Rotational Motion: Kinematics |
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Level 3: 35%-60%
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The instantaneous angular position of a point on a rotating wheel is given by the equation,
\(\theta(t)=2t^{3}-6t^{2}\)
The torque on the wheel becomes zero at:
\(\theta(t)=2t^{3}-6t^{2}\)
The torque on the wheel becomes zero at:
| 1. | \(t=0.5\) s | 2. | \(t=0.25\) s |
| 3. | \(t=2\) s | 4. | \(t=1\) s |
Subtopic: Rotational Motion: Kinematics |
79%
Level 2: 60%+
AIPMT - 2011
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A body is in pure rotation. The linear speed \(v\) of a particle, the distance \(r\) of the particle from the axis and the angular velocity \(\omega\) of the body are related as \(w=\dfrac{v}{r}\). Thus:
1. \(w\propto\dfrac{1}{r}\)
2. \(w\propto\ r\)
3. \(w=0\)
4. \(w\) is independent of \(r\)
Subtopic: Rotational Motion: Kinematics |
60%
Level 2: 60%+
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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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Level 1: 80%+
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When a disc rotates with uniform angular velocity, which of the following is not true?
| 1. | the sense of rotation remains the same. |
| 2. | the orientation of the axis of rotation remains the same. |
| 3. | the speed of rotation is non-zero and remains the same. |
| 4. | the angular acceleration is non-zero and remains the same. |
Subtopic: Rotational Motion: Kinematics |
68%
Level 2: 60%+
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Angular velocity at any time \(t\) of a rotating body is given as \(\omega \left(t\right) = \omega_{0} + \alpha t\). Its magnitude of angular acceleration:
| 1. | is always constant |
| 2. | increases with time |
| 3. | decreases with time |
| 4. | first increases then decreases with time |
Subtopic: Rotational Motion: Kinematics |
75%
Level 2: 60%+
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The angular speed of a flywheel moving with uniform angular acceleration changes from \(1200\) rpm to \(3120\) rpm in \(16\) s. The angular acceleration in rad/s² is:
| 1. | \(104 \pi\) | 2. | \(2\pi\) |
| 3. | \(4\pi\) | 4. | \(12\pi\) |
Subtopic: Rotational Motion: Kinematics |
75%
Level 2: 60%+
NEET - 2022
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A flywheel is accelerated uniformly from rest and rotates through \(5\) rad in the first second. The angle rotated by the flywheel in the next second will be:
1. \(7.5\text{ rad}\)
2. \(15\text{ rad}\)
3. \(20\text{ rad}\)
4. \(30\text{ rad}\)
1. \(7.5\text{ rad}\)
2. \(15\text{ rad}\)
3. \(20\text{ rad}\)
4. \(30\text{ rad}\)
Subtopic: Rotational Motion: Kinematics |
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Level 2: 60%+
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A rod of length \(l\) is rotating with angular speed \(\omega\) about an axis passing through its corner. The area swept by rod in time \(\dfrac {\pi} {2\omega}\) is:
| 1. | \(\pi l^2\) | 2. | \(\dfrac{\pi l^2}{4}\) |
| 3. | \(\dfrac {\pi l^2}{4\omega^2}\) | 4. | \(\dfrac { l^2}{4\pi \omega^2}\) |
Subtopic: Rotational Motion: Kinematics |
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The angular speed of a wheel is increased from \(1200\) rpm to \(2400\) rpm in \(10\) s. If the angular acceleration remains constant, its value is:
1. \(4\pi\) rad s–2
2. \(2\pi\) rad s–2
3. \(4\) rad s–2
4. \(2\) rad s–2
1. \(4\pi\) rad s–2
2. \(2\pi\) rad s–2
3. \(4\) rad s–2
4. \(2\) rad s–2
Subtopic: Rotational Motion: Kinematics |
75%
Level 2: 60%+
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