Q. No.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 |
A body is projected at an angle of \(30^{\circ}\) with the horizontal with a speed of \(30\) m/s. What is the angle made by the velocity vector with the horizontal after \(1.5\) sec? \(\left(g=10~\text{m/s}^2\right)\)
1. \(0^{\circ}\)
2. \(30^{\circ}\)
3. \(60^{\circ}\)
4. \(90^{\circ}\)
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