Projectile motion and uniform circular motion - One Line Questions

1. For a projectile launched at angle $\theta$, the ratio of maximum height to the horizontal range is: $\frac{\tan \theta}{4}$
2. The time of flight of a projectile launched with initial velocity $v_0$ at an angle $ heta$ to the horizontal is given by: $\frac{2 v_0 \sin \theta}{g}$
3. For a particle moving in a circle of radius r with constant speed v, the time period T is given by: $\frac{2\pi r}{v}$
4. If a particle completes one revolution in time T, its angular velocity is: $\frac{2\pi}{T}$
5. The magnitude of centripetal acceleration for a particle of mass m moving with speed v in a circle of radius r is: $\frac{v^2}{r}$
6. For a projectile launched with initial velocity $v_0$ at an angle $ heta$ to the horizontal, what is the maximum height reached? $\frac{v_0^2 \sin^2 \theta}{2g}$
7. What is the horizontal range of a projectile launched with initial velocity $v_0$ at an angle $ heta$ to the horizontal, assuming no air resistance? $\frac{v_0^2 \sin(2\theta)}{g}$
8. For a particle in uniform circular motion, the angular speed $\omega$ and time period T are related by: $\omega = \frac{2\pi}{T}$
9. If a particle is moving in a circle of radius r with angular velocity $\omega$, its centripetal acceleration is: $\omega^2 r$
10. If a projectile is thrown horizontally from a height h with speed u, the time taken to reach the ground is: $\sqrt{\frac{2h}{g}}$
11. The maximum range of a projectile is $R_{max}$. What is the range for an angle of projection of 30 degrees? $R_{max}/2$
12. For a projectile thrown horizontally from height h with speed u, the horizontal distance covered (range) is: $u \sqrt{\frac{2h}{g}}$
13. The angular velocity $\omega$ of a particle in uniform circular motion is related to its linear speed v and radius r by: $v = \omega r$
14. The speed of a particle in uniform circular motion is related to its frequency f by: $v = 2\pi r f$
15. A projectile is launched with velocity $v_0$ at an angle $\theta$ to the horizontal. Its velocity at time t is given by: $v_x = v_0 \cos \theta$, $v_y = v_0 \sin \theta - gt$
16. The position coordinates of a projectile launched from the origin at time t are: $x = (v_0 \cos \theta) t$, $y = (v_0 \sin \theta) t - \frac{1}{2}gt^2$
17. For a projectile launched at an angle $\theta$ to the horizontal, the equation of the trajectory is: $y = x \tan \theta - \frac{gx^2}{2 v_0^2 \cos^2 \theta}$
18. What is the angle between the velocity vector and the acceleration vector at any instant in uniform circular motion? 90 degrees
19. A particle is moving in a circle of radius 5m. If its angular velocity is 2 rad/s, its linear speed is: 10 m/s
20. A particle moves in a circle of radius 10 m with a constant speed of 5 m/s. What is the magnitude of its centripetal acceleration? 2.5 m/s$^2$
21. For a fixed initial speed, the horizontal range of a projectile is maximum when the angle of projection is: 45 degrees
22. For a projectile motion, the horizontal range is zero when the angle of projection is: 0 degrees or 90 degrees
23. In uniform circular motion, the angular acceleration is: Always zero
24. The force required to maintain uniform circular motion is called: Centripetal force
25. What is the velocity of a particle moving in uniform circular motion at any instant? Variable and tangential
26. If two projectiles are launched with the same initial speed at angles $\theta$ and $(90 - \theta)$ degrees to the horizontal, their horizontal ranges are: Equal
27. In projectile motion, the horizontal component of acceleration is: Zero
28. The trajectory of a projectile is a parabola because: Horizontal velocity is constant and vertical acceleration is constant
29. The maximum height reached by a projectile is independent of: Horizontal component of velocity
30. The velocity of a particle in uniform circular motion changes direction at every instant because: Its direction of motion changes
31. A body is revolving in a circle with constant speed. Which of the following quantities is changing? Momentum
32. The centripetal force is proportional to: Mass and square of speed
33. At the highest point of its trajectory, the vertical component of the velocity of a projectile is: Minimum (zero)
34. If a projectile is launched vertically upwards, its trajectory is a straight line. What is its horizontal range? Zero
35. In uniform circular motion, the instantaneous power delivered by the centripetal force is: Zero
36. If a particle starts from rest and moves in uniform circular motion, its initial speed is: Zero
37. In uniform circular motion, the work done by the centripetal force over one complete revolution is: Zero
38. The centripetal acceleration is proportional to: Square of speed
39. The path followed by a projectile under gravity (neglecting air resistance) is a: Parabola
40. If the time of flight of a projectile is T, then the time taken to reach the maximum height is: T/2
41. The acceleration experienced by a particle in uniform circular motion is called: Centripetal acceleration
42. What is the direction of the acceleration vector in uniform circular motion? Towards the center
43. The direction of the centripetal force is always: Towards the center of the circle
44. Which of the following statements is INCORRECT regarding projectile motion (neglecting air resistance)? The kinetic energy is constant.
45. The horizontal component of velocity of a projectile remains constant because: The acceleration is zero
46. Which quantity is conserved in projectile motion if air resistance is neglected? Total mechanical energy
47. In uniform circular motion, the speed of the particle is: Constant
48. Which of the following quantities remains constant for a particle undergoing uniform circular motion? Speed
49. In projectile motion, the vertical component of acceleration is: Constant and equal to -g (downwards)
50. What is the angular displacement in one complete revolution of a particle in uniform circular motion? $2\pi$ radians