Q. No.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. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s
1. \(20\) m/s
2. \(20\sqrt{2}\) m/s
3. \(10 \sqrt{5}\) m/s
4. \(30\) m/s
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 missile is fired for maximum range with an initial velocity of \(20\) m/s, then the maximum height of missile is: (Take \(g=10\) m/s2)
1. \(20\) m
2. \(30\) m
3. \(10\) m
4. \(40\) m
A particle is moving along a circle of radius \(R \) with constant speed \(v_0\). What is the magnitude of change in velocity when the particle goes from point \(A\) to \(B \) as shown?
| 1. | \( 2{v}_0 \sin \frac{\theta}{2} \) | 2. | \(v_0 \sin \frac{\theta}{2} \) |
| 3. | \( 2 v_0 \cos \frac{\theta}{2} \) | 4. | \(v_0 \cos \frac{\theta}{2}\) |
A projectile is projected with speed u at an angle of 30° with the vertical from the ground. The angle between the acceleration of the projectile and its velocity at the time of striking the horizontal ground is:
(1) 30°
(2) 60°
(3) 45°
(4) 0°
Which of the following statements is incorrect?
| 1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
| 2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
| 3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
| 4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |
A man is walking on a horizontal road at a speed of \(4~\text{km/hr}.\) Suddenly, the rain starts vertically downwards with a speed of \(7~\text{km/hr}.\) The magnitude of the relative velocity of the rain with respect to the man is:
1. \(\sqrt{33}~\text{km/hr}\)
2. \(\sqrt{65}~\text{km/hr}\)
3. \(8~\text{km/hr}\)
4. \(4~\text{km/hr}\)
In a uniform circular motion:
(1) Velocity and acceleration remain constant.
(2) Kinetic energy remains constant.
(3) Speed and acceleration changes.
(4) Only velocity changes, acceleration remains constant.
Compared to an ideal projectile motion under gravity, which of the following is incorrect regarding another projectile motion in which air friction is also considered?
| 1. | The time of flight decreases. |
| 2. | Decrease in the horizontal component of velocity continuously. |
| 3. | The angle with horizontal is less at the time of striking the ground compared to the angle of projection with horizontal. |
| 4. | The angle with the vertical is less at the time of striking the ground with respect to the angle of projection with vertical. |
At the highest point of trajectory in the ground to the ground projectile, the angle between gravitational acceleration and momentum is
(1) 30°
(2) 45°
(3) 90°
(4) Data insufficient
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