Q. No.Rain falls vertically at the speed of \(30~\text{m/s}.\) A woman riding a bicycle with a speed of \(10~\text{m/s}\) in the north-to-south direction. What is the direction in which she should hold her umbrella?
[given: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)
1.
\(16^{\circ}\) with the vertical, towards the north
2.
\(18^{\circ}\) with the vertical, towards the north
3.
\(16^{\circ}\) with the vertical, towards the south
4.
\(18^{\circ}\) with the vertical, towards south
[given: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)
1. \(20~\text{min}\)
2. \(18~\text{min}\)
3. \(15~\text{min}\)
4. \(16~\text{min}\)
In a harbor, the wind is blowing at the speed of \(72~\text{km/h},\) and the flag on the mast of a boat anchored in the harbor flutters along the \(N\text-E\) direction. If the boat starts moving at a speed of \(51~\text{km/h}\) to the north, what is the direction of the flag on the mast of the boat?
1. almost due north
2. almost due east
3. almost due west
4. almost due south
The ceiling of a long hall is \(25~\text m\) high. What is the maximum horizontal distance that a ball thrown with a speed of \(40~\text{m/s}\) can go without hitting the ceiling of the hall?
1. \(150.5~\text m\)
2. \(165.6~\text m\)
3. \(145.3~\text m\)
4. \(158.2~\text m\)
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. |
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. \(8.54 ~\text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~{x} \text{-axis}. \)
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. | \(\sqrt2,~45^\circ\) with the \(x\text-\)axis. |
| 2. | \(\sqrt2,~-45^\circ\) with the \(x\text-\)axis. |
| 3. | \(\dfrac1{\sqrt2},~60^\circ\) with the \(x\text-\)axis. |
| 4. | \(\dfrac1{\sqrt2},~-60^\circ\) with the \(x\text-\)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. | \(\vec{v}_{\text {avg }}=\frac{\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |
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