Q. No.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
A man wants to cross a river 600 m wide flowing at 8 m/s in the shortest time. Man has a speed of 6 m/ s in still water. What is the path length covered by the man in the river?
1. Infinite
2. 1 km
3. 100 m
4. 1000 cm
A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\))
| 1. | \(20\) m | 2. | \(10\) m |
| 3. | \(40\) m | 4. | \(400\) m |
A particle is moving along a circular path of radius a with constant angular velocity . The magnitude of displacement of the particle as a function of time t is:
1.
2.
3.
4.
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