- 1(current)
Q. No.Which one of the following statements is not true?
| 1. | The magnitude of a vector is always a scalar. |
| 2. | The average speed of a particle is either greater or equal to the magnitude of the average velocity of the particle over the same interval of time. |
| 3. | Three vectors not lying in a plane can never add up to give a null vector. |
| 4. | Each component of a vector is always a scalar. |
A cyclist starts from the center \(\mathrm{O}\) of a circular park of radius \(1\) km, reaches the edge \(\mathrm{P}\) of the park, then cycles along the circumference, and returns to the center along \(\mathrm{QO}\) as shown in the figure. If the round trip takes \(10\) min, then the average speed of the cyclist is:
1. \(22.42\) km/h
2. \(23.32\) km/h
3. \(21.42\) km/h
4. \(27.12\) km/h
The position of a particle is given by; \(\vec{{r}}=[(3.0 {t} )\hat{{i}}-(2.0 {t}^2) \hat{{j}}+(4.0) \hat{{k}} ]~\text{m},\) where \(t\) is in seconds and the coefficients have the proper units for \(\vec r\) to be in meters. What is the magnitude and direction of the velocity of the particle at \(t=2.0~\text s?\)
1. \(7.56~ \text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~{y} \text{-axis}. \)
2. \(7.56~ \text{m} \text{s}^{-1}, ~70^{\circ}\text{ with} ~{x} \text{-axis}. \)
3. \(8.54 ~\text{m} \text{s}^{-1},~70^{\circ}\text{ with} ~{y} \text{-axis}. \)
4. \(8.54 ~\text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~{x} \text{-axis}. \)
| 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. | \(\vec{v}_{\text {avg }}=\frac{\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |
An aircraft is flying with speed \(v\) at a height of \(3400~\text{m}\) above the ground (As shown in the figure). If the angle subtended at a ground observation point by the aircraft positions \(10.0~\text{s}\) apart is \(30^{\circ}\), what is the speed of the aircraft? ( Take \(\tan15^{\circ} = 0.267\))
1. \(182~\text{m/s}\)
2. \(130~\text{m/s}\)
3. \(192~\text{m/s}\)
4. \(179~\text{m/s}\)
- 1(current)
Q. No.
© 2025 GoodEd Technologies Pvt. Ltd.