Q. No.Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:
1. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | the average velocity is not zero at any time. |
| 2. | average acceleration must always vanish. |
| 3. | displacements in equal time intervals are equal. |
| 4. | equal path lengths are traversed in equal intervals. |
For a particle performing uniform circular motion,
| (a) | the magnitude of particle velocity (speed) remains constant. |
| (b) | particle velocity is always perpendicular to the radius vector. |
| (c) | the direction of acceleration keeps changing as the particle moves. |
| (d) | angular momentum is constant in magnitude but direction keeps changing. |
Choose the correct statement/s:
| 1. | (c), (d) | 2. | (a), (c) |
| 3. | (b), (c) | 4. | (a), (b), (c) |
A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. \(5\) unit
2. \(12\) unit
3. \(13\) unit
4. \(17\) unit
The position of a moving particle at time \(t\) is \(\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:
| 1. | \(\hat{j}-\hat{k}\) | 2. | \(3\hat{i}-4\hat{j}-\hat{k}\) |
| 3. | \(9\hat{i}+36\hat{j}-27\hat{k}\) | 4. | \(32\hat{j}-26\hat{k}\) |
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 \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
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 is moving on a circular path of radius \(R.\) When the particle moves from point \(A\) to \(B\) (angle \( \theta\)), the ratio of the distance to that of the magnitude of the displacement will be:
| 1. | 2. | ||
| 3. | 4. |
|
A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s2 along the north. The velocity of the body just after \(4\) s will be?
| 1. | \(8\) m/s along East. |
| 2. | \(4 \sqrt{2} \) m/s along North-East. |
| 3. | \(8\) m/s along North. |
| 4. | \(4 \sqrt{2} \) m/s along South-East. |
If three coordinates of a particle change according to the equations \(x = 3 t^{2}, y = 2 t , z= 4\), then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. \(2\sqrt{11}~\text{unit}\)
2. \(\sqrt{34}~\text{unit}\)
3. \(40~\text{unit}\)
4. \(2\sqrt{10}~\text{unit}\)
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