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Q. No.A rigid body rotates about a fixed axis with variable angular velocity equal to \(\alpha- \beta t\) at time \(t\), where \(\alpha \) and \(\beta\) are constants. The angle through which it rotates before it comes to rest is:
1.
\( \dfrac{\alpha^{2}}{2 \beta}\)
2.
\( \dfrac{\alpha^{2}- \beta^2}{2 \alpha}\)
3.
\( \dfrac{\alpha^{2}- \beta^2}{2 \beta}\)
4.
\(\alpha (\alpha - \beta) \over 2 \)
Subtopic: Circular Motion |
75%
Level 2: 60%+
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A ball is projected with a velocity of \(10~\text{m/s}\) at an angle of \(60^\circ\) with the vertical direction. Its speed at the highest point of its trajectory will be:
1. \(10~\text{m/s}\)
2. zero
3. \(5\sqrt{3}~\text{m/s}\)
4. \(5~\text{m/s}\)
1. \(10~\text{m/s}\)
2. zero
3. \(5\sqrt{3}~\text{m/s}\)
4. \(5~\text{m/s}\)
Subtopic: Projectile Motion |
61%
Level 2: 60%+
NEET - 2022
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Rain is falling vertically downward with a speed of \(35~\text{m/s}.\) The wind starts blowing after some time with a speed of \(12~\text{m/s}\) in the east to the west direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
Subtopic: Relative Motion |
71%
Level 2: 60%+
NEET - 2022
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Given below are two statements:
| Assertion (A): | When a particle moves in a circle with uniform speed, both its velocity and its acceleration change continuously. |
| Reason (R): | The centripetal acceleration in circular motion is independent of the angular velocity of the particle. |
| 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: Circular Motion |
60%
Level 2: 60%+
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Given below are two statements:
| Assertion (A): | In a two-dimensional motion, there are two accelerations acting on the particle. |
| Reason (R): | Both the components of velocity, i.e., horizontal and vertical, in case of free fall keeps on changing with respect to time. |
| 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: Acceleration |
Level 3: 35%-60%
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A particle moves with a speed \(v\) in a circle of radius \(R.\) The \({x}\text -\)component of the average velocity of the particle in a half-revolution as shown in the figure, is:
1. \(\left(\dfrac{-v}{\pi}\right)\)
2. \(\left(\dfrac{-v}{2 \pi}\right)\)
3. \(\left(\dfrac{-v}{4 \pi}\right)\)
4. \(\left(\dfrac{-2 v}{\pi}\right)\)
1. \(\left(\dfrac{-v}{\pi}\right)\)
2. \(\left(\dfrac{-v}{2 \pi}\right)\)
3. \(\left(\dfrac{-v}{4 \pi}\right)\)
4. \(\left(\dfrac{-2 v}{\pi}\right)\)
Subtopic: Circular Motion |
Level 3: 35%-60%
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Two projectiles are fired from the same point with the same speed at angles of projection \(60^\circ\) and \(30^\circ\) respectively. Which one of the following is true?
| 1. | Their time of flight will be the same. |
| 2. | Their maximum height will be the same. |
| 3. | Their range will be the same. |
| 4. | Their landing velocity will be the same. |
Subtopic: Projectile Motion |
86%
Level 1: 80%+
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Select the correct option based on the statements given below:
| Statement I: | When a projectile is at its highest point, its tangential acceleration is zero. |
| Statement II: | When a projectile is at the highest point of its trajectory, its speed is minimum. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Projectile Motion |
64%
Level 2: 60%+
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A person can throw a ball up to a maximum range of \(100\) m. How high above the ground can he throw the same ball?
1. \(25\) m
2. \(50\) m
3. \(100\) m
4. \(200\) m
1. \(25\) m
2. \(50\) m
3. \(100\) m
4. \(200\) m
Subtopic: Projectile Motion |
Level 3: 35%-60%
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The magnitude of the displacement of a particle moving in a circle of radius \(a\) with constant angular speed \(\omega\) varies with time \(t\) as:
| 1. | \(2a\sin\omega t\) | 2. | \(2a\sin{{\omega t}\over{2}}\) |
| 3. | \(2a\cos\omega t\) | 4. | \(2a\cos{{\omega t}\over{2}}\) |
Subtopic: Circular Motion |
65%
Level 2: 60%+
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