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. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
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: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)
1. | \(16^{\circ}\) with the vertical, towards north |
2. | \(18^{\circ}\) with the vertical, towards north |
3. | \(16^{\circ}\) with the vertical, towards south |
4. | \(18^{\circ}\) 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 \(25\) 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,
\(\overrightarrow{\text{r}}=(3.0 \text{t} \hat{\text{i}}-2.0 \text{t}^2 \hat{\text{j}}+4.0 \hat{\text{k}} )~\text{m}\)
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 \(t=2.0\) s?
1. \(7.56~ \text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~\text{y} \text{-axis}. \)
2. \(7.56~ \text{m} \text{s}^{-1}, ~70^{\circ}\text{ with} ~\text{x} \text{-axis}. \)
3. \(8.54 ~\text{m} \text{s}^{-1},~70^{\circ}\text{ with} ~\text{y} \text{-axis}. \)
4. \(8.54 ~\text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~\text{x} \text{-axis}. \)
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