Q. No.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 \(|\frac{d\vec{v}}{dt}|\neq0\) but \(\frac{d|\vec{v}|}{dt}=0\)
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 \(|\frac{d\vec{v}}{dt}|=0\) but \(\frac{d|\vec{v}|}{dt}\neq0\)
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 m/)
| 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 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 , 37° south to east |
| 2. | 0.25 , 37° west to north |
| 3. | 0.5 , 37° east to north |
| 4. | 0.5 , 37° south to west |
A bus is going to the North at a speed of 30 kmph. It makes a 90° 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-W |
| 3. | 42.4 kmph towards S-W |
| 4. | 42.4 kmph towards N-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 \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| = 0 \) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}} \neq 0 \) |
| 2. | It is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0 \) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 .\) |
| 3. | it is possible to have\(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right|=0\) and \(\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 . \) |
| 4. | It is possible to have \(\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0\) \(\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}} \neq 0 \) |
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/]
| 1. | \(10 \sqrt{3} \) | 2. | \(20 \sqrt{3}\) |
| 3. | 10 | 4. | 0 |
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