Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella? [Given: tan 16º = 0.29 & tan 18º = 0.33]
1. 16º with the vertical, towards north
2. 18º with the vertical, towards north
3. 16º with the vertical, towards south
4. 18º with the vertical, towards south
A man can swim at a speed of \(4.0\) km/h in still water. How long does he take to cross a river \(1.0\) km wide if the river flows steadily at \(3.0\) km/h and he makes his strokes normal to the river current?
1. \(20\) min
2. \(18\) min
3. \(15\) min
4. \(16\) 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 \(\mathrm{N\text-E}\) 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 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall?
1. 150.5 m
2. 165.6 m
3. 145.3 m
4. 158.2 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 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 center. |
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,\(\overrightarrow{\mathrm{r}}=(3.0 \mathrm{t} \hat{\mathrm{i}}-2.0 \mathrm{t}^2 \hat{\mathrm{j}}+4.0 \hat{\mathrm{k}} )~\mathrm{m}\) 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 \(t=2.0\) s?
1. \(7.56 \mathrm{~m} \mathrm{s}^{-1},-70^{\circ}\text{ with} ~\mathrm{y}- \text{axis}. \)
2. \(7.56 \mathrm{~m} \mathrm{s}^{-1}, ~70^{\circ}\text{ with} ~\mathrm{x}- \text{axis}. \)
3. \(8.54 \mathrm{~m} \mathrm{s}^{-1},~70^{\circ}\text{ with} ~\mathrm{y}- \text{axis}. \)
4. \(8.54 \mathrm{~m} \mathrm{s}^{-1},-70^{\circ}\text{ with} ~\mathrm{x}- \text{axis}. \)
A particle starts from the origin at t = 0 sec with a velocity of and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?
1. | 2 s
|
2. | 3 s
|
3. | 4 s
|
4. | 1 s |
1. | \(\sqrt2,~45^\circ\) with the x-axis. |
2. | \(\sqrt2,~-45^\circ\) with the x-axis. |
3. | \(\frac1{\sqrt2},~60^\circ\) with the x-axis. |
4. | \(\frac1{\sqrt2},~-60^\circ\) with the x-axis. |
For any arbitrary motion in space, which of the following relations is true?
1. | \(\vec{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]\) |
2. | \(\vec{v}(t)=\vec{v}(0)+\vec{a} t\) |
3. | \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\overrightarrow{\mathrm{r}}(0)+\overrightarrow{\mathrm{v}}(0) \mathrm{t}+\frac{1}{2} \overrightarrow{\mathrm{a}} \mathrm{t}^2\) |
4. | \(\vec{v}_{\text {avg }}=\frac{\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}\) |