JEE Main - Projectile motion and uniform circular motion Online Test (MCQ Quiz)

1. For a projectile launched with initial velocity $v_0$ at an angle $ heta$ to the horizontal, what is the maximum height reached?

A) $\frac{v_0^2 \sin^2 \theta}{g}$ B) $\frac{v_0^2 \cos^2 \theta}{2g}$ C) $\frac{v_0^2 \sin^2 \theta}{2g}$ D) $\frac{v_0^2 \tan \theta}{g}$

2. 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) $\frac{v_0^2 \sin \theta \cos \theta}{g}$

3. 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) $\frac{v_0 \tan \theta}{g}$

4. 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

5. 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

6. 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

7. 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

8. The path followed by a projectile under gravity (neglecting air resistance) is a:

A) Straight line B) Circle C) Parabola D) Ellipse

9. In projectile motion, the horizontal component of acceleration is:

A) Equal to g B) Zero C) Constant but not zero D) Variable

10. 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

11. 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

12. In uniform circular motion, the speed of the particle is:

A) Variable B) Constant C) Zero D) Zero at the highest point

13. 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

14. The acceleration experienced by a particle in uniform circular motion is called:

A) Tangential acceleration B) Centrifugal acceleration C) Centripetal acceleration D) Linear acceleration

15. 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) $\frac{mr}{v^2}$

16. The force required to maintain uniform circular motion is called:

A) Centrifugal force B) Centripetal force C) Gravitational force D) Frictional force

17. 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

18. 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) $\frac{r}{2\pi v}$

19. 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) $\omega = vr$

20. 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) $\omega r^2$

21. 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) $v_x = v_0 \sin \theta - gt$, $v_y = v_0 \cos \theta$

22. 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) $x = (v_0 \sin \theta) t - \frac{1}{2}gt^2$, $y = (v_0 \cos \theta) t$

23. 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) $y = x \cot \theta + \frac{gx^2}{2 v_0^2 \sin^2 \theta}$

24. 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

25. Which of the following quantities remains constant for a particle undergoing uniform circular motion?

A) Velocity B) Acceleration C) Speed D) Momentum

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. 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) $u \times h$

28. 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

29. 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

30. 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$^2$

31. 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) $2\pi T$

32. 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

33. 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

34. In uniform circular motion, the work done by the centripetal force over one complete revolution is:

A) Positive B) Negative C) Zero D) Maximum

35. 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) $v = \frac{r f}{2\pi}$

36. 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

37. 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

38. 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

39. 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

40. 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) $\frac{2}{\tan \theta}$

41. In uniform circular motion, the instantaneous power delivered by the centripetal force is:

A) Maximum B) Minimum C) Zero D) Variable

42. 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

43. 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

44. If a particle starts from rest and moves in uniform circular motion, its initial speed is:

A) Maximum B) Minimum C) Zero D) Undefined

45. The centripetal acceleration is proportional to:

A) Square of speed B) Inverse square of speed C) Radius D) Inverse of radius

46. 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

47. 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

48. 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) $R_{max}$

49. 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) $\omega = \frac{T}{\pi}$

50. 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

Projectile motion and uniform circular motion - Online Test

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