Which one of the following is not true?
1. | The net acceleration of a particle in a circular motion is always along the radius of the circle towards the center. |
2. |
The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point. |
3. | The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector. |
4. | None of the above. |
A particle starts from the origin at t = 0 sec with a velocity of and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?
1. | 2 s
|
2. | 3 s
|
3. | 4 s
|
4. | 1 s |
For any arbitrary motion in space, which of the following relations is true?
1. | \(\vec{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]\) |
2. | \(\vec{v}(t)=\vec{v}(0)+\vec{a} t\) |
3. | \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\overrightarrow{\mathrm{r}}(0)+\overrightarrow{\mathrm{v}}(0) \mathrm{t}+\frac{1}{2} \overrightarrow{\mathrm{a}} \mathrm{t}^2\) |
4. | \(\vec{v}_{\text {avg }}=\frac{\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |
A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of \(|displacement| \over distance\) will be:
1. 0
2. 1/7
3. 2/7
4. 1/11
Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:
1. | displacement is \(2\pi R\) |
2. | distance covered is \(2R\) |
3. | displacement is zero. |
4. | distance covered is zero. |
A particle projected from origin moves in the x-y plane with a velocity , where and are the unit vectors along the x and y-axis. The equation of path followed by the particle is:
1.
2.
3.
4.
The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by and metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1.
2.
3.
4.
The velocity at the maximum height of a projectile is times its initial velocity of projection (u). Its range on the horizontal plane is:
1.
2.
3.
4.
The equation of a projectile is . Its horizontal range is?
1.
2.
3.
4.
When a particle is projected at some angle to the horizontal, it has a range R and time of flight t1. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is t2, then:
1.
2.
3.
4.