Q. No.Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and the diameter \(AB.\) If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:
1. \(2\)
2. \(2\sqrt{3}\)
3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)
1. \(2\)
2. \(2\sqrt{3}\)
3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)
A particle moves on the curve \(x^2 = 2y\). The angle of its velocity vector with the \(x\)-axis at the point \(\left(1, \frac{1}{2}\right )\) will be:
| 1. | \(30^\circ\) | 2. | \(60^\circ\) |
| 3. | \(45^\circ\) | 4. | \(75^\circ\) |
A particle is moving along a curve. Select the correct statement.
| 1. | If its speed is constant, then it has no acceleration. |
| 2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |
| 3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |
| 4. | If its speed is constant, its acceleration is perpendicular to its velocity. |
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A particle is moving in the \(XY\) plane such that \(x = \left(t^2 -2t\right)~\text m,\) and \(y = \left(2t^2-t\right)~\text m,\) then:
| 1. | the acceleration is zero at \(t=1~\text s.\) |
| 2. | the speed is zero at \(t=0~\text s.\) |
| 3. | the acceleration is always zero. |
| 4. | the speed is \(3~\text{m/s}\) at \(t=1~\text s.\) |
Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |
Which of the following statements is incorrect?
| 1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
| 2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
| 3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
| 4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
If a body is accelerating, then:
| 1. | it must speed up. |
| 2. | it may move at the same speed. |
| 3. | it may move with the same velocity. |
| 4. | it must slow down. |
A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\))
| 1. | \(20\) m | 2. | \(10\) m |
| 3. | \(40\) m | 4. | \(400\) m |
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