Projectile Motion Oscillation, Class 12 Physics MCQ Quiz Test

MCQ 1:
The co-ordinates of a moving particle at any time t are given by x = ct² and y = bt². The speed of the particle is given by

2t(c + b)
2t√(c² – b²)
t√(c² + b²)
2t√(c² + b²)

MCQ 2:
The height y and the distance x along the horizontal at plane of the projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t – 5t²) metre and x = 6t metre where t is in seconds. The velocity with which the projectile is projected is

8 m/s
6 m/s
10 m/s
Data is insufficient

MCQ 3:
A body is thrown at an angle 30° to the horizontal with the velocity of 30 m/s. After 1 sec, its velocity will be (in m/s) (g = 10 m/s²)

10√7
700√10
100√7
√10

MCQ 4:
A particle is moving in a plane with a velocity given by, u = u₀ i + (ωa cos ωt) j , where i and j are unit vectors along x and y-axes respectively. If the particle is at the origin at t = 0, then its displacement from the origin at time t = 3π/2ω will be

MCQ 5:
A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about

2.5 m
5 m
7.5 m
10 m

MCQ 6:
Kalpit and Mukesh are playing with two different balls of masses m and 2m respectively. If Kalpit throws his ball vertically up and Mukesh at an angle θ, both of them stay in our view for the same period. The height attained by the two balls are in the ratio

2 : 1
1 : 1
1 : cos θ
1 : sec θ

MCQ 7:
A projectile is thrown at angle θ and (90° – θ) from the same point with the same velocity 98 m/s. The heights attained by them, if the difference of heights is 50 m will be (in m)

270, 220
300, 250
250, 200
200, 150

MCQ 8:
A particle is projected with a velocity u so that its horizontal range is twice the greatest height attained. The horizontal range is

u²/g
2u²/3g
4u²/5g
u²/2g

MCQ 9:
Mr C.P. Nawani kicked off a football with an initial speed 19.6 m/s at a projection angle 45°. A receiver on the goal line 67.4 m away in the direction of the kick starts running to meet the ball at that instant. What must be his speed so that he could catch the ball before hitting the ground?

2.82 m/s
2/√2 m/s
39.2 m/s
10 m/s

MCQ 10:
A ball 'A' is projected from origin with an initial velocity v₀ = 700 cm/sec in a direction 37° above the horizontal as shown in figure. Another ball 'B' 300 cm from origin on a line 37° above the horizontal is released from rest at the instant A starts. How far will B have fallen when it is hit by A?

9 cm
90 cm
0.9 cm
900 cm

MCQ 11:
A ball is thrown from ground level so as to just clear a wall 4 metres high at a distance of 4 metres and falls at a distance of 14 metres from the wall. The magnitude velocity of the ball will be

√182 m/s
√181 m/s
√185 m/s
√186 m/s

MCQ 12:
A ball is projected from O with an initial velocity 700 cm/s in a direction 37° above the horizontal. A ball B, 500 cm away from O on the line of the initial velocity of A, is released from rest at the instant A is projected. The height through which B falls, before it is hit by A and the direction and magnitude of the velocity A at the time of impact will respectively be
[given g = 10 m/s², sin 37° = 0.6 and cos 37° = 8.0]

250 cm, 28° 42'
255 cm, 27° 43'
245 cm, 20° 44'
300 cm, 27° 43'

MCQ 13:
A ball is thrown horizontally from a height of 20 m. It hits the ground with a velocity three times its initial velocity. The initial velocity of ball is

2 m/s
3 m/s
5 m/s
7 m/s

MCQ 14:
A projectile is thrown from a height of 10 m with a velocity of √2 m/s, the projectile will fall, from the foot of projection, at a distance (g = 10 m/s²)

1 m
2 m
3 m
√2 m

MCQ 15:
Savita throws a ball horizontally with a velocity of 8 m/s from the top of the her building. The ball strikes to her brother Sudhir playing at 12 m away from the building. What is the height of the building?

11 m
10 m
8 m
7 m

MCQ 16:
A body is projected downwards at an angle of 30 ° to the horizontal with a velocity of 9.8 m/s from the top of a tower 29.4 m high. How long will it take before striking the ground

1s
2s
3s
4s

MCQ 17:
A bomb is dropped on an enemy post by an aeroplane flying with a horizontal velocity of 60 km/hr and at a height of 490 m. How far the aeroplane must be from the enemy post at the time of dropping the bomb, so that it may directly hit the target? (g = 9.8 m/s²). What is the trajectory of the bomb as seen by an observer on the earth? What as seen by a person sitting inside the aeroplane?

150/3 m vertical downward, parabola
150/3 m parabola, vertical downward
150/3 m vertical downward, vertical downward
150/3 m parabola, parabola

MCQ 18:
A ball is thrown from the top of a tower with an initial velocity of 10 m/s at an angle of 30° above the horizontal. It hits the ground at a distance of 17.3 m from the base of the tower. The height of the tower (g = 10 m/s²) will be

10 m
12 m
110 m
100 m

MCQ 19:
A person is standing on a truck moving with a constant velocity of 14.7 m/s on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m. What is the speed of the ball as seen from the truck?

9.8 m/s
19.6 m/s
29.4 m/s
24.5 m/s

MCQ 20:
If retardation produced by air resistances to projectile is one-tenth of acceleration due to gravity, the time to reach maximum height approximately

increase by 9%
decrease by 9%
increase by 11%
decrease by 11%

MCQ 21:
Equation of two S.H.M. (Simple Harmonic Motion) are x₁ = 5 sin (2πt + π/4), x₂ = 5 (sin2πt + cos2πt). The ratio of amplitude & phase difference will be

2 : 1, 0
1 : 2, 0
1 : 2, π/2
2 : 1, π/2

MCQ 22:
Two particle executes S.H.M. (Simple Harmonic Motion) in same straight line, Their amplitude & frequency are equal. When their displacement is half of amplitude, they passes each other in opposite direction. Phase difference will be

30°
150°
180°
120°

MCQ 23:
For a simple pendulum, graph between velocity (v) & displacement (x)

Parabolic
Circular
Elliptical
Straight line

MCQ 24:
A particle is executing Simple Harmonic Motion from the mean position at 5cm distance, acceleration is 20cm/sec², then the value of angular velocity will be

2 rad/sec²
4 rad/sec²
10 rad/sec²
15 rad/sec²

MCQ 25:
The maximum velocity of a harmonic oscillator is α and its maximum acceleration is β. Its time period will be

2πα/β
2πβ/α
2παβ
πβ/α

MCQ 26:
If harmonic oscillator have mass 0.8kg, amplitude 1.0 m & time period 11/7 sec then particle velocity & kinetic energy at displacement 0.6m will be

4 J
4.11 J
4.01 J
4.1 J

MCQ 27:
Length of spring 2cm increases, when a body of 1kg mass is suspended from a weightless spring. This body is stretched up to 10cm. Time period of vibration of spring & kinetic energy of spring oscillation will be

2.5 sec, 0.2 J
2.05 sec, 0.28 J
0.28 sec,2.05 J
0.28 sec, 2.5 J

MCQ 28:
A body of mass 0.1 kg is attached to two springs of force constants 8N/m & 2N/m and supported by two rigid supports. If the body is displaced along the length of the spring, the frequency of vibration will be

16 sec^–1
0.16 sec^–1
1.6
1.6 sec^–1

MCQ 29:
One mass m is suspended from a spring. Time period of oscillation is T. Now if spring is divided into n pieces & these are joined in parallel order then time period of oscillation if same mass is suspended.

2π√(n²m/k)
2π√(n²k/m)
2π√(m/n²k)
2π√(k/n²m)

MCQ 30:
Time period of spring mass system will be

2π √(3k/m)
2π √(3m/k)
1/2π √(m/3k)
2π √(m/3k)

MCQ 31:
Periodic time of oscillation T₁ is obtained when a mass is suspended from a spring if another spring is used with same mass then periodic time of oscillation is T₂. Now if this mass is suspended from series combination of above springs then time period will be

√(T₁² – T₂²)
√(T₁ + T₂)
√(T₁² T₂²)
√(T₁² + T₂²)

MCQ 32:
One wooden cylinder of uniform cross section is floating in water vertically. When it is slightly pressed, it oscillates. If l length of cylinder is drowned in water then its time period.

T = 2π √(g/λ)
T = 2π √(m/k)
T = 2π √(k/m)
T = 2π √(λ/g)

MCQ 33:
The velocity acquired by a body moving with uniform acceleration is 20 meter/second in first 2 seconds and 40 m/sec in first 4 sec. The initial velocity will be

0 m/sec
40 m/sec
20 m/sec
None

MCQ 34:
A body moves along the sides AB, BC and CD of a square of side 10 meter with velocity of constant magnitude 3 meter/sec. Its average velocity will be

3 m/sec
0.87 m/sec
1.33 m/sec
None

MCQ 35:
A body covers half the distance with a velocity 10 m/s and remaining half with a velocity 15 m/s along a straight line. The average velocity will be

12 m/s
10 m/s
5 m/s
12.5 m/s

MCQ 36:
A point travelling along a straight line traverse one third the distance with a velocity v₀. The remaining part of the distance was covered with velocity v₁ for half the time and with velocity v₂ for the other half of the time. The mean velocity of the point averaged over the whole time of motion will be

MCQ 37:
A particle moves along the x-axis in such a way that its x-coordinate varies with time according to the equation x = 2 – 5t + 6t². The initial velocity and acceleration will respectively be

5 m/s, 12 m/s²
–12 m/s, –5 m/s²
12, – 5 m/s2²
–5 m/s, 12 m/s²

MCQ 38:
The position of a body with respect to time is given by x = 4t³ – 6t² + 20 t + 12. Acceleration at t = 0 will be

–12 units
12 units
24 units
–24 units

MCQ 39:
A body travels 200 cm in the first two seconds and 220 cm in the next four second. The velocity at the end of the seventh second from the start will be

10 cm/s
5 cm/s
15 cm/s
20 cm/s

MCQ 40:
An α particle travels along the inside of straight hollow tube, 2.0 metre long, of a particle accelerator. Under uniform acceleration, how long is the particle in the tube if it enters at a speed of 1000 m/s and leaves at 9000 m/s

4 × 10^–4 sec
2 × 10^–7 sec
40 × 10^–4 sec
20 × 10^–7 sec

MCQ 41:
A truck starts from rest with an acceleration of 1.5 m/s² while a car 150 m behind starts from rest with an acceleration of 2 m/s². How long will it take before both the truck and car side by side, and how much distance is travelled by each?

2.45 s, 500 m (truck), 650 m (car)
5 s, 450 m (truck), 600 m (car)
24.5 s, 450 m (truck), 600 m (car)
5.3 s, 500 m (truck), 650 m (car)

MCQ 42:
Two car travelling towards each other on a straight road at velocity 10 m/sec and 12 m/sec respectively. When they are 150 m apart, both drivers apply their brakes and each car decelerates at 2 m/sec² until it stops. How far apart will they be when they have both come to a stop?

8.9 m
89 m
809 m
890 m

MCQ 43:
The driver of a train travelling at 115 km/hour sees on the same track 100 m in front of him a slow train travelling in same direction at 25 km/hr. The least retardation that must be applied to the faster train to avoid a collision will be

3.125 m/s²
31.25 m/s²
312.5 m/s²
0.3125 m/s²

MCQ 44:
A car is moving with a velocity of 20 m/sec. The driver sees a stationary truck at a distance of 100 m ahead. After some reaction time Δt he applies the brakes, produces a retardation of 4 m/s². The maximum reaction time to avoid collision will be

5 sec
2.5 sec
4 sec
10 sec

MCQ 45:
An engine driver of a passenger train traveling at 40 m/s sees a goods train, whose last compartment is 250 m ahead on the same track. The goods train is traveling in the same direction as the passenger train, with a constant speed of 20 m/s. The passenger train driver has a reaction time of 0.5 sec. He applies the brakes which cause the train to decelerate at the rate of 1 m/sec2, while the goods train continues with its constant speed. Can the driver save a crash?

Yes, if the distance between the trains before application of brakes is more than 200 m
Yes, if the distance between the trains before application of brakes is more than 250 m
No, if the distance between the trains before application of brakes is more than 200 m
No, if the distance between the trains before application of brakes is more than 250 m

MCQ 46:
A body is falling from a height 'h'. It takes t₁ sec to reach the ground, the time taken to reach the half of the height will be

√2t₁
t₁/2
t₁/√2
2t₁

MCQ 47:
A body thrown up with a velocity reaches a maximum height of 100 m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of

400 m
200 m
100 m
250 m

MCQ 48:
A ball dropped from the top of a building takes 0.5 sec to clear the window of 4.9 m height. What is the height of building above the window?

2.75 m
5.0 m
5.5 m
4.9 m

MCQ 49:
A ball is thrown straight upward with an initial speed of 12 m/sec. After 1 sec velocity & displacement will respectively be

2 m/sec, 7 m
7m, 2 m/sec
2.20 m/s, 7.10 m
None

MCQ 50:
A ball is thrown from ground vertically upward, reaches the roof of a house 100 meters high. At the moment this ball was thrown vertically upward, another ball is dropped from rest vertically downward from the roof of the house. At which height from the ground do the balls pass each other and after what time?

t = 100/√1960 sec , h = 25 m
t = 100/√1690 sec , h = 25 m
t = 200/√1690 sec , h = 75 m
t = 100/√1960 sec , h = 75 m

MCQ 51:
From the foot of a tower 90 m high a stone is thrown up so as to reach the top of the tower. Two second later another stone is dropped from the top of the tower. When and where two stones meet?

22/7 sec later, at 83.6 m
22/7 sec later, at 86.6 m
2.2/7 sec later, at 86.6 m
2.2/7 sec later, at 83.6 m