Classical Mechanics Quizzes: Test Your Understanding

Question 1

In a hypothesis test, the research hypothesis proposes a difference between two groups. If the p-value is less than 0.05, what should you conclude?

Accepted Answer

Reject the null hypothesis and support the research hypothesis.

Answer

Accept the null hypothesis and reject the research hypothesis.

Answer

Fail to reject the null hypothesis and fail to support the research hypothesis.

Answer

Fail to reject the research hypothesis and fail to reject the null hypothesis.

Question 2

In hypothesis testing, what is the term for the probability of incorrectly rejecting the null hypothesis?

Accepted Answer

Alpha

Answer

Beta

Answer

Power

Answer

Confidence

Question 3

What is the symbol representing the probability of making a Type I error?

Accepted Answer

α

Answer

β

Answer

1 - α

Answer

1 - β

Question 4

A study finds that a new anxiety treatment significantly reduces symptoms (p < 0.05). Which conclusion is reasonable?

Accepted Answer

The treatment may help some people with anxiety.

Answer

The treatment is guaranteed to help everyone with anxiety.

Answer

The treatment has no effect on anyone with anxiety.

Answer

The treatment is completely ineffective for everyone with anxiety.

Question 5

In hypothesis testing, what type of error occurs when we reject the null hypothesis, which states there is no significant difference, when it is actually true?

Accepted Answer

Type I error

Answer

Type II error

Answer

Type III error

Question 6

In hypothesis testing, what does a two-tailed p-value represent?

Accepted Answer

The probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

Answer

The probability of rejecting the null hypothesis when it is true.

Answer

The probability of failing to reject the null hypothesis when it is false.

Answer

The probability that the null hypothesis is true.

Question 7

When examining the difference in perceived stress levels between two groups with non-normally distributed data, which of the following tests would be most appropriate?

Accepted Answer

Mann-Whitney U test

Answer

Student's t-test

Answer

Chi-square test

Answer

Pearson's correlation coefficient

Question 8

In a psychology study testing a new depression therapy, researchers found a p-value of 0.04. If they set the significance level at 0.05, what error might they have made?

Accepted Answer

Type I error

Answer

Type II error

Answer

Sampling error

Answer

Measurement error

Question 9

In a closed system, the total linear momentum before a collision is equal to the total linear momentum after the collision. This property is known as:

Accepted Answer

Law of Conservation of Momentum

Answer

Newton's First Law

Answer

Newton's Third Law

Answer

Law of Conservation of Energy

Question 10

Which of the following physical quantities is a vector, meaning it has both magnitude and direction?

Accepted Answer

Velocity

Answer

Mass

Answer

Time

Answer

Temperature

Question 11

The work (W) done by a constant force (F) over a displacement (d) is calculated as:

Accepted Answer

W = Fd

Answer

W = Fv

Answer

W = ma

Answer

W = Et

Question 12

A pendulum of length L is released from a horizontal position. What is the period of oscillation?

Accepted Answer

2π√(L/g)

Answer

π√(L/g)

Answer

2π√(g/L)

Answer

π√(g/L)

Question 13

A rigid body is rotating about a fixed axis with angular velocity ω. What is the kinetic energy of the body?

Accepted Answer

1/2 Iω^2

Answer

Iω

Answer

1/2 I^2ω

Answer

I^2ω

Question 14

Which of Newton's laws of motion states that the acceleration of an object is directly proportional to the net force acting on it?

Accepted Answer

Newton's Second Law

Answer

Newton's First Law

Answer

Newton's Third Law

Answer

Newton's Law of Universal Gravitation

Question 15

According to the principle of momentum conservation, the total momentum of a closed system remains constant.

Accepted Answer

True

Answer

False

Question 16

Which of the following is the correct unit for energy?

Accepted Answer

Joule

Answer

Newton

Answer

Meter

Answer

Second

Question 17

A ball is thrown vertically upward with a velocity 'v'. What is the maximum height it will reach?

Accepted Answer

v^2 / 2g

Answer

v^2 / g

Answer

2v^2 / g

Answer

g^2 / 2v^2

Question 18

A simple pendulum of length 'L' is swinging with a period 'T'. If the length is increased to '4L', what will be the new period?

Accepted Answer

4T

Answer

T

Answer

2T

Answer

T/2

Question 19

Compare elastic and inelastic collisions, explaining the conservation laws that apply to each type.

Accepted Answer

Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum.

Answer

Elastic collisions conserve kinetic energy only, while inelastic collisions conserve only momentum.

Answer

Elastic collisions conserve momentum only, while inelastic collisions conserve both momentum and kinetic energy.

Answer

Both elastic and inelastic collisions conserve both momentum and kinetic energy.

Question 20

A flywheel with a moment of inertia I is spinning at an angular velocity ω. What is the work needed to stop the flywheel?

Accepted Answer

Iω^2/2

Answer

Iω

Answer

2Iω^2

Answer

Iω^3

Question 21

In classical mechanics, chaos refers to the unpredictable behavior of deterministic systems. Explain how this unpredictability arises.

Accepted Answer

Chaos arises due to the extreme sensitivity of deterministic systems to their initial conditions.

Answer

Chaos is caused by external random forces acting on the system.

Answer

Chaos implies that all deterministic systems are inherently unpredictable.

Question 22

According to Newton's second law of motion, the acceleration of an object is directly proportional to which of the following?

Accepted Answer

The force applied to the object

Answer

The mass of the object

Answer

The velocity of the object

Answer

The displacement of the object

Question 23

Which of the following is NOT considered a conserved quantity in classical mechanics?

Accepted Answer

Heat

Answer

Energy

Answer

Momentum

Answer

Angular momentum

Question 24

An object moving with a constant velocity experiences which of the following situations regarding the net force acting on the object?

Accepted Answer

The net force is zero.

Answer

The net force is in the same direction as the velocity.

Answer

The net force is opposite to the direction of velocity.

Answer

The net force is perpendicular to the direction of velocity.

Question 25

Newton's second law of motion states that:

Accepted Answer

The acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

Answer

The force exerted by an object is equal to its mass multiplied by its velocity.

Answer

The displacement of an object is proportional to the force acting on it.

Question 26

A 5-kilogram object is moving at a velocity of 10 meters per second. What is its kinetic energy?

Accepted Answer

250 joules

Answer

5 joules

Answer

50 joules

Answer

100 joules

Question 27

The work-energy theorem states that:

Accepted Answer

The net work done on an object is equal to its change in kinetic energy.

Answer

The momentum of an object is conserved in an isolated system.

Answer

The force acting on an object is equal to its mass multiplied by its velocity.

Question 28

A car is moving on a circular track of radius 100 m with a constant speed of 20 m/s. What is the direction of the centripetal acceleration of the car?

Accepted Answer

Towards the center of the circular track

Answer

In the direction of motion

Answer

Away from the center of the circular track

Answer

Perpendicular to the direction of motion

Question 29

According to Newton's second law of motion, acceleration (a) of an object is:

Accepted Answer

Directly proportional to the net force (F) acting on it

Answer

Inversely proportional to its mass (m)

Answer

Independent of its velocity (v)

Answer

Equal to the force applied

Question 30

Which of the following forces is non-conservative?

Accepted Answer

Friction

Answer

Gravitational force

Answer

Electrostatic force

Answer

Spring force

Question 31

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Temperature

Answer

Time

Answer

Mass

Question 32

The work (W) done by a constant force (F) is:

Accepted Answer

W = F.d (force multiplied by displacement in the direction of force)

Answer

W = F.t (force multiplied by time)

Answer

W = F.v (force multiplied by velocity)

Answer

W = F/d (force divided by displacement)

Question 33

Which of the following is a unit of torque?

Accepted Answer

Newton-meter (Nm)

Answer

Watt (W)

Answer

Joule (J)

Answer

Kilogram (kg)

Question 34

A rigid body is rotating about a fixed axis. Its rotational inertia (I) is:

Accepted Answer

I = Σ(mr²) (sum of the product of mass and square of their distance from the axis of rotation)

Answer

I = ω (angular velocity)

Answer

I = K (kinetic energy)

Answer

I = p (linear momentum)

Question 35

An object of mass 2.5 kg experiences a force of 10 N. Calculate the acceleration of the object.

Accepted Answer

4 m/s² (Newton's second law: F=ma)

Answer

2.5 m/s² (Incorrect calculation: F=ma, a=F/m=10N/2.5kg)

Answer

10 m/s² (Incorrect calculation: F=ma, a=F/m=10N/2.5kg)

Answer

0.25 m/s² (Incorrect calculation: F=ma, a=F/m=10N/2.5kg)

Question 36

A ball is launched vertically upward with a velocity of 10 m/s. Determine the maximum height it will reach. (Neglect air resistance.)

Accepted Answer

5 m (Conservation of energy: Ep=Ek, max height when v=0, Ep=mgh=½mv², h=v²/2g)

Answer

2.5 m (Incorrect calculation: neglecting the effect of gravity on upward motion)

Answer

10 m (Incorrect calculation: neglecting the effect of gravity on upward motion)

Answer

0 m (Incorrect: the ball will have an initial upward velocity and hence reach a positive maximum height)

Question 37

Two objects of masses 5 kg and 10 kg move toward each other with velocities of 2 m/s and 1 m/s, respectively. Find the combined momentum of the system.

Accepted Answer

12 kg-m/s (Momentum of a system remains constant: p_total=p_1+p_2)

Answer

7 kg-m/s (Incorrect calculation: momentum is a vector quantity, so direction matters)

Answer

17 kg-m/s (Incorrect calculation: momentum is a vector quantity, so direction matters)

Answer

25 kg-m/s (Incorrect calculation: momentum is a vector quantity, so direction matters)

Question 38

Which of the following forces is non-conservative?

Accepted Answer

Friction

Answer

Electrostatic force

Answer

Spring force

Answer

Gravitational force

Question 39

A simple harmonic oscillator has a frequency of 5 Hz. Calculate its period of oscillation.

Accepted Answer

0.2 s (Period and frequency are inversely related: T=1/f)

Answer

0.1 s (Incorrect calculation: T=1/f)

Answer

5 s (Incorrect calculation: T=1/f)

Question 40

Which is a unit of energy?

Accepted Answer

Joule (J)

Answer

Meter (m)

Answer

Newton (N)

Answer

Kilogram (kg)

Question 41

A car travels 100 km in 2 hours. Determine the car's average speed.

Accepted Answer

50 km/h (Average speed=distance/time)

Answer

25 km/h (Incorrect calculation: average speed=distance/time)

Answer

100 km/h (Incorrect: average speed considers the total distance covered, not just the distance in 1 hour)

Answer

200 km/h (Incorrect calculation: average speed=distance/time)

Question 42

Which of the following energy types is not considered mechanical energy?

Accepted Answer

Thermal energy

Answer

Potential energy

Answer

Kinetic energy

Question 43

A pendulum swings with an amplitude of 10 cm. What is the maximum potential energy it can attain?

Accepted Answer

5 mJ (Potential energy at max amplitude: Ep=mgh, h=A)

Answer

10 mJ (Incorrect: potential energy is zero at the mean position, not the maximum amplitude)

Answer

20 mJ (Incorrect calculation: Ep=mgh, h=A)

Answer

15 mJ (Incorrect calculation: Ep=mgh, h=A)

Question 44

Which statement is NOT a law of thermodynamics?

Accepted Answer

The law of conservation of momentum

Answer

The first law of thermodynamics

Answer

The second law of thermodynamics

Answer

The third law of thermodynamics

Question 45

A car of mass 1000 kg is traveling at a velocity of 20 m/s. What is its kinetic energy?

Accepted Answer

100,000 J

Answer

200,000 J

Answer

50,000 J

Answer

40,000 J

Question 46

A ball is launched vertically upward at a velocity of 10 m/s from the ground. What is its maximum height?

Accepted Answer

5 m

Answer

2.5 m

Answer

20 m

Answer

10 m

Question 47

A force of 10 N is applied to an object with a mass of 2 kg. What is the acceleration of the object?

Accepted Answer

5 m/s²

Answer

10 m/s²

Answer

2 m/s²

Question 48

A system is said to be in equilibrium when the net force acting on it is:

Accepted Answer

Zero

Answer

Negative

Answer

Positive

Question 49

Which of the following physical quantities is a scalar?

Accepted Answer

Mass

Answer

Force

Answer

Velocity

Question 50

The work done by a force is calculated as:

Accepted Answer

Force x Displacement x cosine of the angle between them

Answer

Force / Displacement

Answer

Displacement / Force

Answer

Force x Displacement

Question 51

The momentum of a system is defined as:

Accepted Answer

Mass multiplied by Velocity

Answer

Work / Time

Answer

Energy / Mass

Answer

Force x Time

Question 52

In an elastic collision, which of the following quantities remains conserved?

Accepted Answer

Kinetic energy and Momentum

Answer

Momentum only

Answer

Kinetic energy only

Answer

Neither kinetic energy nor momentum

Question 53

A particle moves in a straight line with constant speed. Which of the following statements is true?

Accepted Answer

Its acceleration is zero.

Answer

Its velocity is zero.

Answer

Its kinetic energy is zero.

Answer

Its momentum is zero.

Question 54

A ball is thrown vertically upward with an initial velocity of 10 m/s. What is its maximum height?

Accepted Answer

5 m

Answer

15 m

Answer

10 m

Answer

20 m

Question 55

A pendulum of length L swings with a period of T. What is the period of a pendulum of length 4L?

Accepted Answer

2T

Answer

4T

Answer

T/4

Answer

T/2

Question 56

A spring has a spring constant of 100 N/m. How much work is done in stretching the spring by 0.1 m?

Accepted Answer

0.5 J

Answer

1 J

Answer

5 J

Answer

2 J

Question 57

A block of mass 2 kg slides down a frictionless inclined plane of height 1 m and length 2 m. What is its speed at the bottom?

Accepted Answer

4.43 m/s

Answer

6.67 m/s

Answer

2.22 m/s

Question 58

A projectile is fired with an initial velocity of 100 m/s at an angle of 30 degrees above the horizontal. What is its range?

Accepted Answer

866 m

Answer

1732 m

Answer

433 m

Answer

2598 m

Question 59

A rigid body rotates about a fixed axis with an angular velocity of 10 rad/s. What is its kinetic energy if its moment of inertia is 2 kg m^2?

Accepted Answer

100 J

Answer

50 J

Answer

400 J

Answer

200 J