Q. No.A particle moving on a curved path possesses a velocity of \(3\) m/s towards the north at an instant. After \(10\) s, it is moving with speed \(4\) m/s towards the west. The average acceleration of the particle is:
1.
\(0.25~\text{m/s}^2,\) \(37^{\circ}\) south to east.
2.
\(0.25~\text{m/s}^2,\) \(37^{\circ}\) west to north.
3.
\(0.5~\text{m/s}^2,\) \(37^{\circ}\) east to north.
4.
\(0.5~\text{m/s}^2,\) \(37^{\circ}\) south to west.
A man can row a boat with a speed of \(10\) kmph in still water. The river flows at \(6\) kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width \(1\) km is:
1. \(\frac{1}{8}~\text{h}\)
2. \(\frac{1}{4}~\text{h}\)
3. \(\frac{1}{2}~\text{h}\)
4. \(1~\text{h}\)
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. | \(30\) kmph towards \(W\) |
| 2. | \(30\) kmph towards \(S\text-W\) |
| 3. | \(42.4\) kmph towards \(S\text-W\) |
| 4. | \(42.4\) kmph towards \(N\text-W\) |
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. | \(32\hat{j}-26\hat{k}\) |
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