Q. No.A particle has an initial velocity \(\overrightarrow{u} = \left(4 \hat{i} - 5 \hat{j}\right)\) m/s and it is moving with an acceleration \(\overrightarrow{a} = \left(\frac{1}{4} \hat{i} + \frac{1}{5} \hat{j}\right)\text{m/s}^{2}\). Velocity of the particle at \(t=2\) s will be:
1. \((6\hat i -4\hat j)~\text{m/s}\)
2. \((4.5\hat i -4.5\hat j)~\text{m/s}\)
3. \((4.5\hat i -4.6\hat j)~\text{m/s}\)
4. \((6\hat i -4.6\hat j)~\text{m/s}\)
1. \((6\hat i -4\hat j)~\text{m/s}\)
2. \((4.5\hat i -4.5\hat j)~\text{m/s}\)
3. \((4.5\hat i -4.6\hat j)~\text{m/s}\)
4. \((6\hat i -4.6\hat j)~\text{m/s}\)
A body is projected with a velocity of \(\left(3 \hat{i} + 4 \hat{j}\right)\text{m/s}\). The maximum height attained by the projectile is: (\(g=10\) ms–2)
| 1. | \(0.8\) m | 2. | \(8\) m |
| 3. | \(4\) m | 4. | \(0.4\) m |
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. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
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 centre. |
| 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 \(10\hat j~\text{m/s}\) and moves in the \(x\text-y\) plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)~\text{m/s}^2\). At what time is the \(x\text-\)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. | \(\overrightarrow{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\overrightarrow{v}\left(t_1\right)+\overrightarrow{v}\left(t_2\right)\right]\) |
| 2. | \(\overrightarrow{v}(t)=\overrightarrow{v}(0)+\overrightarrow{a} t\) |
| 3. | \(\overrightarrow{r}({t})=\overrightarrow{r}(0)+\overrightarrow{v}(0){t}+\frac{1}{2} \overrightarrow{a}{t}^2\) |
| 4. | \(\overrightarrow{v}_{\text {avg }}=\frac{\left[\overrightarrow{r}\left(t_2\right)-\overrightarrow{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |
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. \(\frac{1}{7}\)
3. \(\frac{2}{7}\)
4. \(\frac{1}{11}\)
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 \(x\text-y\) plane with a velocity \(\overrightarrow{v} = 3 \hat{i} + 6 x \hat{j}\), where \(\hat i\) and \(\hat j\) are the unit vectors along the \(x\) and \(y\text-\)axis. The equation of path followed by the particle is:
1. \(y=x^2\)
2. \(y=\frac{1}{x^2}\)
3. \(y=2x^2\)
4. \(y=\frac{1}{x}\)
© 2024 GoodEd Technologies Pvt. Ltd.