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 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
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 |
A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of \(|displacement| \over distance\) will be:
1. 0
2. 1/7
3. 2/7
4. 1/11
Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:
1. | displacement is \(2\pi R\) |
2. | distance covered is \(2R\) |
3. | displacement is zero. |
4. | distance covered is zero. |
A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of 5 m/s at an angle of \(120^\circ\) with the flow. The speed of the flow must be:
1. \(2.5\) m/s
2. \(3\) m/s
3. \(4\) m/s
4. \(1.5\) m/s
A car with a vertical windshield moves in a rain storm at a speed of \(40\) km/hr. The rain drops fall vertically with a constant speed of \(20\) m/s. The angle at which raindrops strike the windshield is:
1.
2.
3.
4.
A particle projected from origin moves in the x-y plane with a velocity , where and are the unit vectors along the x and y-axis. The equation of path followed by the particle is:
1.
2.
3.
4.
The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by and metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1.
2.
3.
4.