A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). How much high above the ground, can the cricketer throw the same ball?
1. \(50~\text{m}\)
2. \(60~\text{m}\)
3. \(75~\text{m}\)
4. \(100~\text{m}\)
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Then the ratio of its centripetal acceleration with the acceleration due to gravity is:
1. 5.4:1
2. 6.4:1
3. 4:1
4. 1:1
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.
2.
3.
4.
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. \(8.54 \mathrm{~m} \mathrm{s}^{-1},-70^{\circ}\text{ with} ~\mathrm{x}- \text{axis}. \)