Master Mechanics 2: Enhance Your Understanding with Interactive Quizzes

Question 1

A particle of mass m moves in a circular path of radius R with an angular velocity ω in a non-inertial reference frame rotating with the same angular velocity ω. What forces act on the particle?

Accepted Answer

Both centripetal and Coriolis forces

Answer

Centripetal force only

Answer

Coriolis force only

Question 2

A particle of mass m is projected vertically upwards with an initial velocity u. Neglecting air resistance, what is its acceleration at the highest point of its trajectory?

Accepted Answer

It is equal to zero.

Answer

It is equal to g.

Answer

It is equal to -g.

Answer

It cannot be determined from the information given.

Question 3

A spring has a spring constant of k. It is stretched by a distance x. What is the potential energy stored in the spring?

Accepted Answer

PE = kx^2/2

Answer

PE = kx

Answer

PE = k^2x/2

Answer

PE = kx^3/2

Question 4

The period of an object undergoing simple harmonic motion is T. Express its frequency in terms of T.

Accepted Answer

f = 1/T

Answer

f = T/2

Answer

f = 2T

Answer

f = T^2

Question 5

A planet of mass M orbits a star of mass m in a circular path of radius r. The gravitational force between the planet and the star is:

Accepted Answer

F = GMm/r^2

Answer

F = Gm^2/r^2

Answer

F = GmM/r

Answer

F = GMm/2r^2

Question 6

A projectile is launched at an angle θ to the horizontal with a velocity u. What is its horizontal range?

Accepted Answer

R = u^2sinθcosθ/g

Answer

R = u^2cosθsinθ/g

Answer

R = u^2sin^2θ/g

Answer

R = u^2cos^2θ/g

Question 7

A particle is moving in a circle of radius r with a constant speed v. What is its centripetal acceleration?

Accepted Answer

ac = v^2/r

Answer

ac = rv^2

Answer

ac = v/r

Answer

ac = r/v

Question 8

A particle moves with constant acceleration in a straight line. Which graph accurately represents the relationship between velocity and time for this particle?

Accepted Answer

A linear graph with a positive gradient

Answer

A linear graph with a negative gradient

Answer

A parabolic graph opening upwards

Answer

A parabolic graph opening downwards

Question 9

A block with a mass of 2.0 kg slides down a frictionless inclined plane inclined at an angle of 30° to the horizontal. Calculate the acceleration of the block.

Accepted Answer

9.81 sin 30° m/s²

Answer

9.81 m/s²

Answer

19.62 m/s²

Answer

4.91 m/s²

Question 10

Calculate the period of a simple harmonic oscillator with a frequency of 2 Hz.

Accepted Answer

0.5 s

Answer

0.25 s

Answer

1 s

Answer

2 s

Question 11

Two particles, one with a mass 'm' and the other with a mass '2m,' move with equal speeds. Which particle possesses greater kinetic energy?

Accepted Answer

The particle with mass '2m'

Answer

The particle with mass 'm'

Answer

Both particles have the same kinetic energy

Answer

The answer depends on the speed of the particles

Question 12

Identify the conservative force from the list below:

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Viscous damping

Question 13

A projectile is launched with a velocity of 20 m/s at an angle of 30° to the horizontal. Determine the horizontal range of the projectile.

Accepted Answer

20.4 m

Answer

10.2 m

Answer

30.6 m

Answer

40.8 m

Question 14

A car accelerates from rest to a speed of 100 m/s in 10 s. Calculate its acceleration.

Accepted Answer

10 m/s²

Answer

2 m/s²

Answer

100 m/s²

Answer

1000 m/s²

Question 15

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Time

Answer

Temperature

Question 16

A particle of mass m is in motion with velocity v. Which expression represents the kinetic energy of the particle?

Accepted Answer

1/2 mv²

Answer

mv²

Answer

2mv²

Answer

1/2 m²v

Question 17

A block of mass 10 kg is sliding down a frictionless inclined plane inclined at an angle of 30 degrees to the horizontal. Calculate the acceleration of the block. (Use g = 9.81 m/s²)

Accepted Answer

4.91 m/s²

Answer

9.81 m/s²

Answer

2.45 m/s²

Answer

1.23 m/s²

Question 18

The acceleration due to gravity on the Earth's surface is approximately:

Accepted Answer

9.81 m/s²

Answer

10 m/s²

Answer

10.2 m/s²

Answer

11.2 m/s²

Question 19

According to the inverse square law of gravitation, the gravitational force between two objects is:

Accepted Answer

Inversely proportional to the square of the distance between them

Answer

Directly proportional to the distance between them

Answer

Inversely proportional to the distance between them

Answer

Inversely proportional to the cube of the distance between them

Question 20

The work done by a constant force acting on an object is equal to:

Accepted Answer

The force multiplied by the distance moved in the direction of the force

Answer

The force multiplied by the distance moved perpendicular to the force

Answer

The force multiplied by the time taken to move the object

Answer

The force divided by the distance moved in the direction of the force

Question 21

If the mass of a particle in uniform motion is doubled, its kinetic energy will:

Accepted Answer

Be quadrupled

Answer

Remain unchanged

Answer

Be halved

Answer

Be doubled

Question 22

A spring with a spring constant of 100 N/m is stretched by 5 cm. What is the stored elastic potential energy in the spring?

Accepted Answer

0.25 J

Answer

0.125 J

Answer

0.5 J

Answer

1 J

Question 23

A simple pendulum of length 1 m has a mass of 1 kg attached to its end. What is the time period of oscillation of the pendulum?

Accepted Answer

1 s

Answer

0.5 s

Answer

2 s

Answer

4 s

Question 24

A body is moving with a constant speed in a circular path. Identify the force acting on the body.

Accepted Answer

Centripetal force

Answer

Centrifugal force

Answer

Gravitational force

Answer

Frictional force

Question 25

State the mathematical representation of the gravitational force between two point masses m1 and m2 separated by a distance r.

Accepted Answer

F = Gm₁m₂/r²

Answer

F = Gm₁m₂r²

Answer

F = Gm₂/m₁r²

Answer

F = Gm₁/m₂r²

Question 26

The work done by a constant force acting on a body moving through a displacement is represented by the equation:

Accepted Answer

W = Fs

Answer

W = F/s

Answer

W = s/F

Answer

W = F^2s

Question 27

Which of the following is a scalar quantity?

Accepted Answer

Displacement

Answer

Velocity

Answer

Acceleration

Answer

Momentum

Question 28

Which of the following correctly states Newton's second law of motion?

Accepted Answer

F = ma

Answer

F = mv

Answer

F = 1/2mv^2

Answer

F = mg

Question 29

Which equation correctly describes the motion of a simple harmonic oscillator?

Accepted Answer

a = -ω^2x

Answer

a = ωx

Answer

a = -x/ω

Answer

a = ω^2x

Question 30

Calculate the gravitational force between two point masses of 1 kg and 2 kg separated by a distance of 1 m:

Accepted Answer

1.33 x 10^-10 N

Answer

6.67 x 10^-11 N

Answer

2.67 x 10^-10 N

Answer

5.33 x 10^-10 N

Question 31

The formula for conservation of energy in mechanics is:

Accepted Answer

KE + PE = constant

Answer

KE - PE = constant

Answer

KE/PE = constant

Answer

PE/KE = constant

Question 32

What is the SI unit of energy?

Accepted Answer

Joule

Answer

Newton

Answer

Watt

Answer

Ampere

Question 33

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 34

What is the coefficient of restitution between two colliding bodies if the separation velocity is half of the approach velocity?

Accepted Answer

0.5

Answer

0

Answer

1

Answer

2

Question 35

A star of mass M has a planet of mass m orbiting it. The gravitational force between them is:

Accepted Answer

GMm/(r²)

Answer

Gm²/(r²)

Answer

Gm/(r²)

Answer

GM/(r²)

Question 36

A force of 50 N is applied to a stationary body of mass 2 kg. What is the resulting acceleration of the body?

Accepted Answer

5 m/s²

Answer

2.5 m/s²

Answer

10 m/s²

Answer

20 m/s²

Question 37

A projectile is launched at an angle of 45° with an initial velocity of 20 m/s. What is its maximum vertical height above the launch point?

Accepted Answer

10.2 m

Answer

5.1 m

Answer

20.4 m

Answer

40.8 m

Question 38

A body of mass 'm' is moving with velocity 'v'. If the kinetic energy of the body increases by 'x%', what is the percentage increase in its velocity?

Accepted Answer

(√(x) - 1) * 100%

Answer

√(x)%

Answer

(x/2) * 100%

Answer

(x/100) * 100%

Question 39

A body is moving in a circular path of radius 'r' with tangential velocity 'v'. What is the centripetal force, 'F', acting on the body?

Accepted Answer

F = mv^2/r

Answer

F = mv^2/2r

Answer

F = 2mv^2/r

Answer

F = mv/r

Question 40

A simple harmonic oscillator has a frequency 'f' and amplitude 'A'. What is the maximum velocity, 'v', of the oscillator?

Accepted Answer

v = 2πfA

Answer

v = πfA

Answer

v = fA

Answer

v = 1/2 πfA

Question 41

A projectile is launched with an initial velocity 'u' at an angle 'θ' to the horizontal. Calculate the range of the projectile.

Accepted Answer

u²sin(2θ)/g

Answer

u²cos(2θ)/g

Answer

u²sin(θ)/g

Answer

u²cos(θ)/g

Question 42

A ball is thrown vertically upwards. At its peak height, its velocity is:

Accepted Answer

Zero

Answer

Maximum

Answer

Constant

Answer

Minimum

Question 43

A block slides down a frictionless inclined plane that makes an angle 'θ' with the horizontal. Calculate the acceleration of the block.

Accepted Answer

gsinθ

Answer

gcosθ

Answer

g

Answer

0

Question 44

Two particles of equal mass undergo a head-on elastic collision. After the collision, the particles move:

Accepted Answer

In opposite directions, with equal speed

Answer

In the same direction, with equal speed

Answer

In the same direction, with unequal speed

Answer

In opposite directions, with unequal speed

Question 45

A satellite orbits a planet in a circular path. Which quantity is conserved?

Accepted Answer

Angular momentum

Answer

Kinetic energy

Answer

Potential energy

Answer

Total energy

Question 46

Revised: Two masses, m1 and m2, are connected by a light, inextensible string passing over a smooth pulley. If m1 is greater than m2, what is the acceleration of the system?

Accepted Answer

(m1 - m2)g / (m1 + m2)

Answer

(m1 + m2)g / (m1 - m2)

Answer

g / (m1 + m2)

Answer

(m1 + m2)g

Question 47

Revised: A simple pendulum of length l is displaced from its equilibrium position by an angle θ. What is the angular frequency of the pendulum?

Accepted Answer

√(g / l)

Answer

√(l / g)

Answer

g / l

Answer

l / g

Question 48

Revised: A mass, m, is attached to a spring with spring constant, k. The system is displaced from its equilibrium position by a distance, x. What is the potential energy stored in the spring?

Accepted Answer

1/2 kx^2

Answer

kx^2

Answer

kx / 2

Answer

1/2 kx

Question 49

Revised: A system of two particles with masses m1 and m2 is moving with velocities u1 and u2, respectively. What is the momentum of the system?

Accepted Answer

m1u1 + m2u2

Answer

m1u1 - m2u2

Answer

(m1 + m2)u1

Answer

(m1 + m2)u2

Question 50

A satellite of mass 'm' is orbiting the Earth in a circular path. What is the gravitational force exerted on the satellite by the Earth?

Accepted Answer

GmM/r^2

Answer

Gmr^2/M

Answer

Gm^2/r^3

Answer

Gm/r

Question 51

A force of 10 N acts on a 2 kg particle initially at rest. What is the kinetic energy of the particle after 5 seconds?

Accepted Answer

25 J

Answer

15 J

Answer

50 J

Answer

100 J

Question 52

A particle of mass 'm' is projected vertically upwards with an initial velocity 'u'. What is the maximum height 'h' attained by the particle?

Accepted Answer

u^2 / (2g)

Answer

u^4 / (2g)

Answer

u^4 / (4g)

Answer

u^2 / (4g)

Question 53

A block of mass 'm' rests on a rough horizontal surface with a coefficient of friction 'μ'. What is the minimum force required to start the block moving?

Accepted Answer

μmg

Answer

μm

Answer

2μmg

Answer

mg

Question 54

A spring with spring constant 'k' is stretched by a distance 'x'. What is the potential energy 'PE' stored in the spring?

Accepted Answer

1/2 k x^2

Answer

k x

Answer

1/4 k x^2

Answer

2k x^2

Question 55

A body of mass 'm' moves in a straight line with a constant velocity 'v'. What is the kinetic energy 'KE' of the body?

Accepted Answer

1/2 mv^2

Answer

1/4 mv^2

Answer

2mv^2

Answer

mv

Question 56

A satellite of mass 'm' orbits the Earth in a circular path of radius 'r'. What is the gravitational force 'F' acting on the satellite?

Accepted Answer

GmMr/r^2

Answer

GmMr

Answer

Gmr^2/M

Question 57

A simple harmonic oscillator has a period 'T' and an amplitude 'A'. What is the maximum velocity 'v' of the oscillator?

Accepted Answer

2πA/T

Answer

4πA/T

Answer

A/T

Answer

πA/T

Question 58

A ball is launched vertically upwards with an initial velocity of 10 m/s. Determine the maximum height reached by the ball.

Accepted Answer

5.1 m

Answer

10 m

Answer

1.25 m

Answer

2.5 m

Question 59

A ball is thrown vertically upwards with an initial velocity of 20 m/s. What is its maximum height, assuming negligible air resistance (g = 9.8 m/s²) ?

Accepted Answer

20.4 m

Answer

40.8 m

Answer

10.2 m

Answer

102 m

Question 60

A 2 kg object moving at 5 m/s collides head-on with a stationary 3 kg object. If the collision is perfectly inelastic, what is the velocity of the combined mass after the collision?

Accepted Answer

2 m/s

Answer

3 m/s

Answer

7 m/s

Answer

1 m/s

Question 61

A simple pendulum has a period of 2 seconds. What is the length of the pendulum (g = 9.8 m/s²)?

Accepted Answer

0.99 m

Answer

3.96 m

Answer

0.50 m

Answer

1.98 m

Question 62

Two identical springs, each with a spring constant k, are connected in series. What is the effective spring constant of the combination?

Accepted Answer

k/2

Answer

k

Answer

2k

Answer

4k

Question 63

A 5 kg object is located at a height of 10 m above the ground. What is its gravitational potential energy relative to the ground (g = 9.8 m/s²)?

Accepted Answer

490 J

Answer

245 J

Answer

98 J

Answer

980 J