Q. No.Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |
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 man is walking on a horizontal road with a speed of \(4\) km/h. Suddenly, the rain starts vertically downwards with a speed of \(7\) km/h. The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}\) km/h
2. \(\sqrt{65}\) km/h
3. \(8\) km/h
4. \(4\) km/h
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 \(10\) 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 \(N\text-W\) |
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