Two particles move from A to C and A to D on a circle of radius R and diameter AB. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:
1. 2
2.
3.
4.
A particle moves on the curve \(x^2 = 2y\). The angle of its velocity vector with the x-axis at the point \(\left(1, \frac{1}{2}\right )\) will be:
1. | \(30^\circ\) | 2. | \(60^\circ\) |
3. | \(45^\circ\) | 4. | \(75^\circ\) |
A particle is moving along a curve. Select the correct statement.
1. | If its speed is constant, then it has no acceleration. |
2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |
3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |
4. | If its speed is constant, its acceleration is perpendicular to its velocity. |
A car is moving along east at 10 m/s and a bus is moving along north at 10 m/s. The velocity of the car with respect to the bus is along:
1. | North-East | 2. | South-East |
3. | North-West | 4. | South-West |
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}\). The trajectory of the particle is correctly shown in the figure:
1. | 2. | ||
3. | 4. |
A particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:
1. | Acceleration is zero at t = 1 sec |
2. | Speed is zero at t = 0 sec |
3. | Acceleration is always zero |
4. | Speed is 3 m/s at t = 1 sec |
It is raining at 20 m/s in still air. Now a wind starts blowing with speed 10 m/s in the north direction. If a cyclist starts moving at 10 m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be
1. 20 m/s
2. m/s
3. m/s
4. 30 m/s
River of width 500 m is flowing at a speed of 10 m/s. A swimmer can swim at a speed of 10 m/s in still water. If he starts swimming at an angle of 120° with the flow direction, then the distance he travels along the river while crossing the river is:
1. 250 m
2. m
3. m
4. 500 m
Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is moving along a circle of radius \(R \) with constant speed \(\mathrm{v}_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
1. | \( 2 \mathrm{v}_0 \sin \frac{\theta}{2} \) | 1. | \( \mathrm{v}_0 \sin \frac{\theta}{2} \) |
3. | \( 2 \mathrm{v}_0 \cos \frac{\theta}{2} \) | 4. | \( \mathrm{v}_0 \cos \frac{\theta}{2}\) |