Q. No.A man is walking on a horizontal road at a speed of \(4~\text{km/hr}.\) Suddenly, the rain starts vertically downwards with a speed of \(7~\text{km/hr}.\) The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}~\text{km/hr}\)
2. \(\sqrt{65}~\text{km/hr}\)
3. \(8~\text{km/hr}\)
4. \(4~\text{km/hr}\)
1. \(\sqrt{33}~\text{km/hr}\)
2. \(\sqrt{65}~\text{km/hr}\)
3. \(8~\text{km/hr}\)
4. \(4~\text{km/hr}\)
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 |
An object of mass m is projected from the ground with a momentum \(p\) at such an angle that its maximum height is \(\frac{1}{4}\)th of its horizontal range. Its minimum kinetic energy in its path will be:
| 1. | \(\frac{p^2}{8 m} \) | 2. | \(\frac{p^2}{4 m} \) |
| 3. | \(\frac{3 p^2}{4 m} \) | 4. | \(\frac{p^2}{m}\) |
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 \(10~\text{kmph}\) in still water. The river flows at \(6~\text{kmph}.\) If he crosses the river from one bank to the other along the shortest possible path, the time taken to cross the river of width \(1~\text{km}\) is:
1. \(\frac{1}{8}~\text{hr}\)
2. \(\frac{1}{4}~\text{hr}\)
3. \(\frac{1}{2}~\text{hr}\)
4. \(1~\text{hr}\)
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 \(\frac{{d} \overrightarrow{{v}}}{{dt}} \neq 0 \) |
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