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. | \(v_0 \cos \frac{\theta}{2}\) |
An open trolley is moving on a horizontal road with constant velocity \(v_1\). A man on the trolley throws a ball vertically upward (with respect to trolley) with velocity \(v_2\). Select the correct statement.
1. | Time of flight of the ball to a man on the ground and the man on the trolley will be different. |
2. | Maximum height attained by the ball for both men will be different. |
3. | Horizontal range of the ball for both men will be different. |
4. | Horizontal range of the ball for both men will be the same. |
Two stones are thrown simultaneously from the top of a building horizontally but in opposite directions, they will be moving perpendicular to each other say after time t, then t is equal to ___________. The initial speeds of stones are respectively and acceleration due to gravity is g.
1.
2.
3.
4.
Two projectiles projected with the same speed at angles and (90° - ) from the same point, then is equal to: (where symbols have their usual meanings)
1.
2.
3.
4.
A projectile is projected from the ground with speed 20 m/s at an angle 30° with vertical. The radius of curvature of the path of a projectile, when velocity makes 30° with horizontal is (g = 10 m/)
(1) 8.5 m
(2) 15.4 m
(3) 26.2 m
(4) 32.6 m
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. \(4~\text{km/hr}\)
A particle of mass 6 kg moves with an initial velocity of m/s. A constant force of N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, when its y-coordinate again becomes zero is given by
(1) 6.0 m
(2) 12.8 m
(3) 8 m
(4) 25.6 m