Q. No.A particle starts from the origin at t=0 and moves in the x-y plane with a constant acceleration 'a' in the y direction. Its equation of motion is . The x component of its velocity (at t=0) will be:
1. variable
2.
3.
4.
A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h. Width of the river is 1 km. The minimum time taken for a round trip will be
1. 5 min
2. 60 min
3. 20 min
4. 30 min
A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity of 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.
1. 30° with downstream
2. 60° with downstream
3. 120° with downstream
4. South
Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:
| 1. | \(20 \times 10^8 \mathrm{~m} / \mathrm{s}^2 \) | 2. | \(8 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) |
| 3. | \(120 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) | 4. | \(4 \times 10^8 \mathrm{~m} / \mathrm{s}^2\) |
In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is:
| 1. | 3.14 m/s | 2. | 2.0 m/s |
| 3. | 1.0 m/s | 4. | Zero |
The angle turned by a body undergoing circular motion depends on the time as given by the equation, . It can be deduced that the angular acceleration of the body is?
1. θ1
2. θ2
3. 2θ1
4. 2θ2
A particle is moving eastwards with velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is?
| 1. | Zero |
| 2. | \(\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^2 \) toward north-west |
| 3. | \(\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^2 \) toward north-east |
| 4. | \(\frac{1}{2} m / s^2 \) toward north-west |
A vector is turned without a change in its length through a small angle The value of and are, respectively:
| 1. | 0, adθ | 2. | dθ, 0 |
| 3. | 0, 0 | 4. | None of these |
A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\) \((6\) m, \(7\) m) at time \(t=2\) s and \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:
| 1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
| 3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
The coordinates of a moving particle at a time t, are given by, x=5 sin 10t, y=5 cos 10t. It can be deduced that the speed of the particle will be:
| 1. | 25 units | 2. | 50 units |
| 3. | 10 units | 4. | 30 units |
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