Q. No.A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:
1.
\(30~\text{kmph}\) towards \(\mathrm{W}\)
2.
\(30~\text{kmph}\) towards \(\mathrm{S\text-W}\)
3.
\(42.4~\text{kmph}\) towards \(\mathrm{S\text-W}\)
4.
\(42.4~\text{kmph}\) towards \(\mathrm{N\text-W}\)
Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)
| 1. | The faster one |
| 2. | The slower one |
| 3. | Depends on masses |
| 4. | Both will reach simultaneously |
An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:
| 1. | \(1200\) m | 2. | \(1300\) m |
| 3. | \(1400\) m | 4. | \(1500\) m |
Select the incorrect statement:
| 1. | It is possible to have \(\left|\frac{{d} \overrightarrow{v}}{dt}\right| = 0 \) and \(\frac{{d}|\overrightarrow{v}|}{{dt}} \neq 0 \) |
| 2. | It is possible to have\(\left|\frac{{d} \overrightarrow{{v}}}{{dt}}\right| \neq 0 \) and \(\frac{{d}|\overrightarrow{{v}}|}{dt}=0 .\) |
| 3. | it is possible to have\(\left|\frac{{d} \overrightarrow{v}}{{dt}}\right|=0\) and \(\frac{{d}|\overrightarrow{{v}}|}{dt}=0 . \) |
| 4. | It is possible to have \(\left|\frac{{d} \overrightarrow{{v}}}{{dt}}\right| \neq 0\) and \(\frac{{d} \overrightarrow{{v}}}{{dt}} \neq 0 \) |
A particle of mass \(2\) kg is moving in a circular path with a constant speed of \(10\) m/s. The change in the magnitude of velocity when a particle travels from \(P\) to \(Q\) will be: [assume the radius of the circle is \(10/\pi^2]\)
| 1. | \(10 \sqrt{3} \) | 2. | \(20 \sqrt{3}\) |
| 3. | \(10\) | 4. | \(0\) |
To the captain of a ship \(A\) travelling with velocity \(\overrightarrow{v_{A}} = \left( 3 \hat{i} - 4 \hat{j} \right)\) km/h, a second ship \(B\) appears to have a velocity \(\overrightarrow{v_{B}} = \left(5 \hat{i} +12 \hat{j} \right)\) km/h. What is the true velocity of the ship \(B\)?
1. \(2 \hat{i} + 16 \hat{j}\) km/h
2. \(13 \hat{i} + 8 \hat{j}\) km/h
3. \(- 2 \hat{i} - 16 \hat{j}\) km/h
4. none of these
An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at \(x=-2~\text{m}\), its velocity is \(-(4~\text{m/s})\hat j.\) What is the object's acceleration when it is at \(y= 2~\text{m}\)?
1. \(- 8~\text{m/s}^{2} \hat j\)
2. \(- 8~\text{m/s}^{2} \hat i\)
3. \(- 4~\text{m/s}^{2} \hat j\)
4. \(- 4~\text{m/s}^{2} \hat i\)
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. | \(32\hat{j}-26\hat{k}\) |
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
Balls \(A\) and \(B\) are thrown from two points lying on the same horizontal plane separated by a distance of \(120\) m. Which of the following statements is correct?
| 1. | The balls can never meet. |
| 2. | The balls can meet if the ball \(B\) is thrown \(1\) s later. |
| 3. | The two balls meet at a height of \(45\) m. |
| 4. | None of the above |
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