Q. No.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 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. \((6\hat i -4.6\hat j)~\text{m/s}\)
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. \(y=\frac{1}{x}\)
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