Q. No.A particle is moving along a curve. Select the correct statement.
1.
If its speed is constant, then it has no acceleration.
2.
If its speed is increasing, then the acceleration of the particle is along its direction of motion.
3.
If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion.
4.
If its speed is constant, its acceleration is perpendicular to its velocity.
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}\). The trajectory of the particle is correctly shown in the figure:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:
| 1. | Acceleration is zero at t = 1 sec |
| 2. | Speed is zero at t = 0 sec |
| 3. | Acceleration is always zero |
| 4. | Speed is 3 m/s at t = 1 sec |
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
A particle is moving along a circle of radius \(R \) with constant speed \(\mathrm{v}_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2 \mathrm{v}_0 \sin \frac{\theta}{2} \) | 1. | \( \mathrm{v}_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 \mathrm{v}_0 \cos \frac{\theta}{2} \) | 4. | \( \mathrm{v}_0 \cos \frac{\theta}{2}\) |
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 \(|\frac{d\vec{v}}{dt}|\neq0\) 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 |
© 2024 GoodEd Technologies Pvt. Ltd.