Q. No.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 \(25\) s, 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 \(16~\text{m}\)?
1. \(2\) s
2. \(3\) s
3. \(4\) s
4. \(1\) s
| 1. | \(\vec{v}_{\text {avg }}=\frac{1}{2}\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]\) |
| 2. | \(\vec{v}(t)=\vec{v}(0)+\vec{a} t\) |
| 3. | \(\vec{r}({t})=\vec{r}(0)+\vec{v}(0){t}+\frac{1}{2} \vec{a}{t}^2\) |
| 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. \(\dfrac{1}{7}\)
3. \(\dfrac{2}{7}\)
4. \(\dfrac{1}{11}\)
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 is projected from the origin and moves in the \(xy\text-\)plane with velocity:
\(\vec{v} = 3 \hat{i} + 6 x \hat{j},\)
where \(\hat i\) and \(\hat j\) are unit vectors along the \(x\) and \(y\text-\)axes, respectively. Which of the following represents the equation of the trajectory of the particle?
| 1. | \(y=x^2\) | 2. | \(y=\dfrac{1}{x^2}\) |
| 3. | \(y=2x^2\) | 4. | \(y=\dfrac{1}{x}\) |
The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by
\(y =4 t - 2 t^{2}~ \text{m}\) and \(x =3t\) 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. \(30^{\circ}\)
2. \(37^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)
The velocity at the maximum height of a projectile is \(\frac{\sqrt{3}}{2}\) times its initial velocity of projection \((u)\). Its range on the horizontal plane is:
1. \(\frac{\sqrt{3} u^{2}}{2 g}\)
2. \(\frac{3 u^{2}}{2 g}\)
3. \(\frac{3 u^{2}}{ g}\)
4. \(\frac{u^{2}}{2 g}\)
The equation of a projectile is \(y = ax -bx^{2}\). Its horizontal range is?
1. \(\frac{a}{b}\)
2. \(\frac{b}{a}\)
3. \(a+b\)
4. \(b-a\)
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