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Q. No.If the range of a gun which fires a shell with muzzle speed \(v,\) is \(R,\) then the angle of elevation of the gun is:
1.
\({\cos}^{{-}{1}}\left({\dfrac{{v}^{2}}{Rg}}\right)\)
2.
\({\cos}^{{-}{1}}\left({\dfrac{Rg}{{v}^{2}}}\right)\)
3.
\(\dfrac{1}{2}{\sin}^{{-}{1}}\left({\dfrac{{v}^{2}}{Rg}}\right)\)
4.
\(\dfrac{1}{2}{\sin}^{{-}{1}}\left({\dfrac{Rg}{{v}^{2}}}\right)\)
Subtopic: Projectile Motion |
71%
From NCERT
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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 |
89%
From NCERT
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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 |
66%
From NCERT
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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. \( \frac{\alpha^{2}}{2 \beta}\)
2. \( \frac{\alpha^{2}- \beta^2}{2 \alpha}\)
3. \( \frac{\alpha^{2}- \beta^2}{2 \beta}\)
4. \(\alpha (\alpha - \beta) \over 2 \)
1. \( \frac{\alpha^{2}}{2 \beta}\)
2. \( \frac{\alpha^{2}- \beta^2}{2 \alpha}\)
3. \( \frac{\alpha^{2}- \beta^2}{2 \beta}\)
4. \(\alpha (\alpha - \beta) \over 2 \)
Subtopic: Circular Motion |
74%
From NCERT
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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%
From NCERT
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%
From NCERT
NEET - 2022
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Given below are two statements:
| Assertion (A): | When a particle moves in a circle with a uniform speed, both its velocity and acceleration change. |
| Reason (R): | The centripetal acceleration in circular motion is independent of the angular velocity of the body. |
| 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 |
59%
From NCERT
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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 |
From NCERT
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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 |
From NCERT
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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%
From NCERT
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