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