Projectile motion and uniform circular motion - Question Bank

1. Which of the following statements is INCORRECT regarding projectile motion (neglecting air resistance)?
A) The acceleration is constant.
B) The velocity is never zero.
C) The kinetic energy is constant.
D) The range depends on the launch angle.
2. A body is revolving in a circle with constant speed. Which of the following quantities is changing?
A) Kinetic energy
B) Momentum
C) Angular momentum
D) Speed
3. For a particle in uniform circular motion, the angular speed $\omega$ and time period T are related by:
A) $\omega = \frac{2\pi}{T}$
B) $\omega = \frac{T}{2\pi}$
C) $\omega = \pi T$
D) $\omega = \frac{T}{\pi}$
4. The maximum range of a projectile is $R_{max}$. What is the range for an angle of projection of 30 degrees?
A) $R_{max}/2$
B) $3R_{max}/4$
C) $R_{max}/4$
D) $R_{max}$
5. If a particle moves with constant speed in a curved path, its acceleration must be:
A) Zero
B) Along the direction of motion
C) Perpendicular to the direction of motion
D) Opposite to the direction of motion
6. The centripetal force is proportional to:
A) Mass and speed
B) Mass and square of speed
C) Radius and speed
D) Square of radius and mass
7. The centripetal acceleration is proportional to:
A) Square of speed
B) Inverse square of speed
C) Radius
D) Inverse of radius
8. If a particle starts from rest and moves in uniform circular motion, its initial speed is:
A) Maximum
B) Minimum
C) Zero
D) Undefined
9. The horizontal component of velocity of a projectile remains constant because:
A) There is no force acting horizontally
B) The net force is zero
C) The acceleration is zero
D) Newton's first law applies
10. Which quantity is conserved in projectile motion if air resistance is neglected?
A) Total mechanical energy
B) Momentum
C) Kinetic energy
D) Vertical component of velocity
11. In uniform circular motion, the instantaneous power delivered by the centripetal force is:
A) Maximum
B) Minimum
C) Zero
D) Variable
12. For a projectile launched at angle $\theta$, the ratio of maximum height to the horizontal range is:
A) $\frac{\tan \theta}{4}$
B) $\frac{1}{2 \tan \theta}$
C) $\frac{\tan \theta}{2}$
D) $\frac{2}{\tan \theta}$
13. If the time of flight of a projectile is T, then the time taken to reach the maximum height is:
A) T
B) T/2
C) 2T
D) T/4
14. What is the angle between the velocity vector and the acceleration vector at any instant in uniform circular motion?
A) 0 degrees
B) 90 degrees
C) 180 degrees
D) Variable
15. The trajectory of a projectile is a parabola because:
A) Horizontal velocity is constant and vertical acceleration is constant
B) Horizontal velocity is variable and vertical acceleration is constant
C) Horizontal velocity is constant and vertical acceleration is variable
D) Both horizontal and vertical components of velocity are constant
16. A particle is moving in a circle of radius 5m. If its angular velocity is 2 rad/s, its linear speed is:
A) 2.5 m/s
B) 5 m/s
C) 10 m/s
D) 20 m/s
17. The speed of a particle in uniform circular motion is related to its frequency f by:
A) $v = 2\pi r f$
B) $v = \frac{f}{2\pi r}$
C) $v = \frac{2\pi f}{r}$
D) $v = \frac{r f}{2\pi}$
18. In uniform circular motion, the work done by the centripetal force over one complete revolution is:
A) Positive
B) Negative
C) Zero
D) Maximum
19. For a projectile motion, the horizontal range is zero when the angle of projection is:
A) 30 degrees
B) 45 degrees
C) 60 degrees
D) 0 degrees or 90 degrees
20. The maximum height reached by a projectile is independent of:
A) Initial vertical velocity
B) Acceleration due to gravity
C) Horizontal component of velocity
D) Square of the sine of the launch angle
21. If a particle completes one revolution in time T, its angular velocity is:
A) $\frac{2\pi}{T}$
B) $\frac{T}{2\pi}$
C) $\frac{\pi}{T}$
D) $2\pi T$
22. 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?
A) 2.5 m/s$^2$
B) 5 m/s$^2$
C) 10 m/s$^2$
D) 25 m/s$^2$
23. What is the angular displacement in one complete revolution of a particle in uniform circular motion?
A) Zero
B) $\pi$ radians
C) $2\pi$ radians
D) Depends on speed
24. The velocity of a particle in uniform circular motion changes direction at every instant because:
A) Its speed changes
B) Its acceleration changes
C) Its momentum changes
D) Its direction of motion changes
25. For a projectile thrown horizontally from height h with speed u, the horizontal distance covered (range) is:
A) $u \sqrt{\frac{2h}{g}}$
B) $u \sqrt{\frac{g}{2h}}$
C) $h \sqrt{\frac{2u}{g}}$
D) $u \times h$
26. If a projectile is thrown horizontally from a height h with speed u, the time taken to reach the ground is:
A) $\sqrt{\frac{2h}{g}}$
B) $\frac{h}{u}$
C) $\sqrt{\frac{2u}{g}}$
D) $\frac{2h}{u}$
27. Which of the following quantities remains constant for a particle undergoing uniform circular motion?
A) Velocity
B) Acceleration
C) Speed
D) Momentum
28. In uniform circular motion, the angular acceleration is:
A) Always zero
B) Non-zero and constant
C) Non-zero and variable
D) Zero only at the highest point
29. For a projectile launched at an angle $\theta$ to the horizontal, the equation of the trajectory is:
A) $y = x \tan \theta - \frac{gx^2}{2 v_0^2 \cos^2 \theta}$
B) $y = x \tan \theta + \frac{gx^2}{2 v_0^2 \cos^2 \theta}$
C) $y = x \cot \theta - \frac{gx^2}{2 v_0^2 \sin^2 \theta}$
D) $y = x \cot \theta + \frac{gx^2}{2 v_0^2 \sin^2 \theta}$
30. The position coordinates of a projectile launched from the origin at time t are:
A) $x = (v_0 \cos \theta) t$, $y = (v_0 \sin \theta) t - \frac{1}{2}gt^2$
B) $x = (v_0 \sin \theta) t$, $y = (v_0 \cos \theta) t - \frac{1}{2}gt^2$
C) $x = (v_0 \cos \theta) t - \frac{1}{2}gt^2$, $y = (v_0 \sin \theta) t$
D) $x = (v_0 \sin \theta) t - \frac{1}{2}gt^2$, $y = (v_0 \cos \theta) t$
31. A projectile is launched with velocity $v_0$ at an angle $\theta$ to the horizontal. Its velocity at time t is given by:
A) $v_x = v_0 \cos \theta$, $v_y = v_0 \sin \theta - gt$
B) $v_x = v_0 \sin \theta$, $v_y = v_0 \cos \theta - gt$
C) $v_x = v_0 \cos \theta - gt$, $v_y = v_0 \sin \theta$
D) $v_x = v_0 \sin \theta - gt$, $v_y = v_0 \cos \theta$
32. If a particle is moving in a circle of radius r with angular velocity $\omega$, its centripetal acceleration is:
A) $\omega^2 r$
B) $\frac{\omega^2}{r}$
C) $\frac{\omega}{r^2}$
D) $\omega r^2$
33. The angular velocity $\omega$ of a particle in uniform circular motion is related to its linear speed v and radius r by:
A) $v = \omega r$
B) $v = \frac{\omega}{r}$
C) $v = \frac{r}{\omega}$
D) $\omega = vr$
34. For a particle moving in a circle of radius r with constant speed v, the time period T is given by:
A) $\frac{2\pi r}{v}$
B) $\frac{v}{2\pi r}$
C) $\frac{2\pi v}{r}$
D) $\frac{r}{2\pi v}$
35. The direction of the centripetal force is always:
A) Tangential to the circular path
B) Opposite to the direction of motion
C) Towards the center of the circle
D) Away from the center of the circle
36. The force required to maintain uniform circular motion is called:
A) Centrifugal force
B) Centripetal force
C) Gravitational force
D) Frictional force
37. The magnitude of centripetal acceleration for a particle of mass m moving with speed v in a circle of radius r is:
A) $\frac{v^2}{r}$
B) $\frac{r^2}{v}$
C) $\frac{mv^2}{r}$
D) $\frac{mr}{v^2}$
38. The acceleration experienced by a particle in uniform circular motion is called:
A) Tangential acceleration
B) Centrifugal acceleration
C) Centripetal acceleration
D) Linear acceleration
39. What is the direction of the acceleration vector in uniform circular motion?
A) Tangential to the circle
B) Away from the center
C) Towards the center
D) Along the velocity vector
40. In uniform circular motion, the speed of the particle is:
A) Variable
B) Constant
C) Zero
D) Zero at the highest point
41. What is the velocity of a particle moving in uniform circular motion at any instant?
A) Constant and tangential
B) Constant and radial
C) Variable and tangential
D) Variable and radial
42. In projectile motion, the vertical component of acceleration is:
A) Zero
B) Constant and equal to -g (downwards)
C) Variable
D) Maximum at the highest point
43. In projectile motion, the horizontal component of acceleration is:
A) Equal to g
B) Zero
C) Constant but not zero
D) Variable
44. The path followed by a projectile under gravity (neglecting air resistance) is a:
A) Straight line
B) Circle
C) Parabola
D) Ellipse
45. If two projectiles are launched with the same initial speed at angles $\theta$ and $(90 - \theta)$ degrees to the horizontal, their horizontal ranges are:
A) Different
B) Equal
C) Zero
D) Maximum
46. For a fixed initial speed, the horizontal range of a projectile is maximum when the angle of projection is:
A) 30 degrees
B) 45 degrees
C) 60 degrees
D) 90 degrees
47. If a projectile is launched vertically upwards, its trajectory is a straight line. What is its horizontal range?
A) Maximum
B) Zero
C) Depends on initial velocity
D) Depends on height
48. At the highest point of its trajectory, the vertical component of the velocity of a projectile is:
A) Maximum
B) Minimum (zero)
C) Equal to the horizontal component
D) Equal to the initial vertical velocity
49. The time of flight of a projectile launched with initial velocity $v_0$ at an angle $ heta$ to the horizontal is given by:
A) $\frac{2 v_0 \sin \theta}{g}$
B) $\frac{v_0 \sin \theta}{g}$
C) $\frac{2 v_0 \cos \theta}{g}$
D) $\frac{v_0 \tan \theta}{g}$
50. 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?
A) $\frac{v_0^2 \sin(2\theta)}{g}$
B) $\frac{v_0^2 \cos(2\theta)}{g}$
C) $\frac{v_0^2 \tan \theta}{g}$
D) $\frac{v_0^2 \sin \theta \cos \theta}{g}$
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