Q. No.Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:
1.
2.
3.
4.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle at a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of the acceleration of the stone?
1. 8.1 ms-2
2. 7.7 ms-2
3. 8.7 ms-2
4. 9.9 ms-2
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.
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