Further Mechanics 1 Quizzes: Master Advanced Mechanics Concepts

Question 1

A block of mass m slides down a frictionless inclined plane at an angle θ to the horizontal. Calculate the acceleration of the block.

Accepted Answer

`gsinθ`

Answer

`msinθ`

Answer

`gcosθ`

Answer

`g`

Question 2

A particle initially at rest starts moving in a straight line with constant acceleration. The displacement of the particle after time t is:

Accepted Answer

0.5 * a * t^2

Answer

a * t

Answer

a * t^2

Answer

0.25 * a * t^2

Question 3

A simple pendulum of length 1 m has a period of oscillation of 2 s. Determine the acceleration due to gravity.

Accepted Answer

9.8 m/s²

Answer

19.6 m/s²

Answer

39.2 m/s²

Answer

78.4 m/s²

Question 4

A machine has an efficiency of 50%. If the input power is 100 W, determine the output power.

Accepted Answer

50 W

Answer

100 W

Answer

150 W

Answer

200 W

Question 5

Which physical quantity is a vector?

Accepted Answer

Acceleration

Answer

Speed

Answer

Temperature

Answer

Mass

Question 6

A force of 10 N acts on a 2 kg body for 5 seconds. What is the change in momentum of the body?

Accepted Answer

10 kg m/s

Answer

5 kg m/s

Answer

25 kg m/s

Answer

50 kg m/s

Question 7

What is the work done to bring a 10 kg body moving at 5 m/s to rest?

Accepted Answer

125 J

Answer

25 J

Answer

50 J

Answer

250 J

Question 8

A rigid body rotates about a fixed axis with a constant angular velocity. How is the angular velocity related to the linear velocity of a point on the body?

Accepted Answer

v = ωr

Answer

ω = v/r

Answer

ω = rv

Answer

v = r/ω

Question 9

How do elastic and inelastic collisions differ in terms of momentum and kinetic energy?

Accepted Answer

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

Answer

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

Answer

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

Question 10

Which physical quantity is considered a scalar?

Accepted Answer

Displacement

Answer

Velocity

Answer

Acceleration

Answer

Force

Question 11

A simple pendulum has a length of 1 m and a period of 2 seconds. Calculate the acceleration due to gravity at its location.

Accepted Answer

9.81 m/s²

Answer

4.91 m/s²

Answer

2.45 m/s²

Answer

1.23 m/s²

Question 12

Which of the following is not a valid unit of energy?

Accepted Answer

Kilogram-meter

Answer

Joule

Answer

Newton-meter

Answer

Watt-second

Question 13

A car of mass 1000 kg is moving at a speed of 20 m/s. What is the kinetic energy of the car?

Accepted Answer

20,000 J

Answer

10,000 J

Answer

50,000 J

Answer

100,000 J

Question 14

A spring of constant k = 100 N/m is stretched by 0.2 m from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

2 J

Answer

1 J

Answer

5 J

Answer

10 J

Question 15

A block of mass 'm' is released from rest at the top of a frictionless inclined plane of length 'L' and height 'h'. Determine the velocity of the block at the bottom of the plane.

Accepted Answer

√(2gh) m/s

Answer

√(gh) m/s

Answer

gh m/s

Answer

2gh m/s

Question 16

A spring with spring constant 'k' is stretched a distance 'x' from its equilibrium position. Calculate the elastic potential energy stored in the spring.

Accepted Answer

1/2kx^2 J

Answer

kx J

Answer

1/4kx^2 J

Answer

2kx^2 J

Question 17

A car is travelling at a constant speed of 30 m/s. If the coefficient of kinetic friction between the car's tires and the road is 0.5, calculate the force of friction acting on the car.

Accepted Answer

900 N

Answer

450 N

Answer

1350 N

Answer

1800 N

Question 18

A ball is launched vertically upward with an initial velocity of 10 m/s. Considering air resistance, which statement accurately describes the ball's motion?

Accepted Answer

The ball's maximum height will be less than 10 meters.

Accepted Answer

The time taken for the ball to reach its maximum height will increase due to air resistance.

Answer

The ball will experience constant acceleration during both its upward and downward motion.

Answer

At its maximum height, the ball will have a constant, non-zero speed.

Question 19

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Answer

Velocity

Answer

Acceleration

Answer

Force

Question 20

A particle is moving with a velocity of (6, 8) m/s. What is the magnitude of the velocity?

Accepted Answer

14 m/s

Answer

2 m/s

Answer

10 m/s

Answer

18 m/s

Question 21

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 22

Which physical quantity is measured in Newton-seconds?

Accepted Answer

Momentum

Answer

Force

Answer

Energy

Answer

Power

Question 23

A simple pendulum has a length of 1 m and a mass of 0.5 kg. What is its time period, assuming small oscillations?

Accepted Answer

2 s

Answer

1 s

Answer

3 s

Answer

4 s

Question 24

In an elastic collision, which physical quantities are conserved?

Accepted Answer

Both kinetic energy and momentum

Answer

Kinetic energy only

Answer

Momentum only

Answer

Neither kinetic energy nor momentum

Question 25

A projectile is dropped from a height 'h' above the ground. Just before impact, what is its velocity?

Accepted Answer

v = √(2gh)

Answer

v = √(gh)

Answer

v = 2gh

Answer

v = gh

Question 26

A force of 10 Newtons is applied over a distance of 5 meters. How much work is done?

Accepted Answer

50 Joules

Answer

5 Joules

Answer

10 Joules

Answer

100 Joules

Question 27

A pendulum of length 1m is released from a horizontal position. What will be its velocity at the lowest point?

Accepted Answer

√(2g)

Answer

√(g)

Answer

2g

Answer

g

Question 28

Calculate the work done by a constant force F acting on a body through a displacement s.

Accepted Answer

Fs

Answer

Fs/2

Answer

F/s

Answer

s/F

Question 29

A 2 kg object is dropped from a height of 10 meters. Neglecting air resistance, what will be its velocity just before it hits the ground?

Accepted Answer

14.14 m/s

Answer

10 m/s

Answer

20 m/s

Answer

28.28 m/s

Question 30

Which of the following physical quantities is a vector?

Accepted Answer

Acceleration

Answer

Speed

Answer

Time

Answer

Mass

Question 31

Which of the following expressions represents the work done by a force?

Accepted Answer

W = F × Δd

Answer

W = F ÷ Δd

Answer

W = F + Δd

Answer

W = F - Δd

Question 32

A 10 kg object is acted upon by a force of 20 N. What is the acceleration produced?

Accepted Answer

2 m/s²

Answer

0.5 m/s²

Answer

10 m/s²

Answer

20 m/s²

Question 33

Which of the following forces is non-conservative?

Accepted Answer

Friction

Answer

Gravity

Answer

Tension

Answer

Spring force

Question 34

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

Accepted Answer

Both kinetic energy and momentum

Answer

Kinetic energy only

Answer

Momentum only

Answer

Neither kinetic energy nor momentum

Question 35

The moment of inertia of a solid sphere of radius R about its diameter is:

Accepted Answer

2MR²/3

Answer

2MR²/5

Answer

MR²/2

Answer

MR²

Question 36

Which of the following formulas correctly describes the centripetal force acting on an object moving in a circular path?

Accepted Answer

Fc = mv²/r

Answer

Fc = mvr

Answer

Fc = mv

Answer

Fc = mr²/v

Question 37

A ball of mass 0.5 kg is thrown vertically upwards with a velocity of 10 m/s. Determine the maximum height reached by the ball.

Accepted Answer

10.2 m

Answer

20.4 m

Answer

15.3 m

Answer

5.1 m

Question 38

A projectile is launched with a velocity of 50 m/s at an angle of 30° to the horizontal. Calculate the horizontal component of the velocity.

Accepted Answer

43.3 m/s

Answer

25.0 m/s

Answer

75.0 m/s

Answer

60.0 m/s

Question 39

A car of mass 1000 kg travels at a constant speed of 20 m/s around a circular track of radius 50 m. What is the magnitude of the centripetal force acting on the car?

Accepted Answer

4000 N

Answer

2000 N

Answer

8000 N

Answer

1000 N

Question 40

A particle of mass 0.5 kg is moving in a circular path of radius 2 m with a speed of 5 m/s. What is the angular velocity of the particle?

Accepted Answer

2.5 rad/s

Answer

5 rad/s

Answer

10 rad/s

Answer

1.25 rad/s

Question 41

A particle is projected vertically upwards with an initial velocity of 20 m/s. What is the maximum height reached by the particle? (Take g = 10 m/s²)

Accepted Answer

20 m

Answer

40 m

Answer

10 m

Answer

50 m

Question 42

A car of mass 1000 kg is travelling at a constant speed of 20 m/s. What is the kinetic energy of the car?

Accepted Answer

200,000 J

Answer

400,000 J

Answer

10,000 J

Answer

1,000,000 J

Question 43

A force of 50 N acts on a body of mass 10 kg. What is the acceleration produced in the body?

Accepted Answer

5 m/s²

Answer

10 m/s²

Answer

2 m/s²

Answer

50 m/s²

Question 44

A ball is thrown horizontally from a cliff with an initial velocity of 10 m/s. If it takes 2 seconds for the ball to hit the ground, what is the horizontal distance travelled by the ball? (Ignore air resistance)

Accepted Answer

20 m

Answer

50 m

Answer

10 m

Answer

40 m

Question 45

A 5 kg block is pulled along a horizontal surface by a force of 20 N. The coefficient of kinetic friction between the block and the surface is 0.2. What is the acceleration of the block? (Take g = 10 m/s²)

Accepted Answer

2 m/s²

Answer

3 m/s²

Answer

1 m/s²

Answer

4 m/s²

Question 46

A roller coaster car of mass 500 kg is at the top of a hill 20 m high. If it rolls down the hill, what is its speed at the bottom of the hill? (Assume no energy losses due to friction or air resistance.)

Accepted Answer

20 m/s

Answer

30 m/s

Answer

40 m/s

Answer

10 m/s

Question 47

A ball is thrown vertically upwards with an initial velocity of 15 m/s. How long does it take to reach its highest point? (Take g = 10 m/s²)

Accepted Answer

1.5 s

Answer

1 s

Answer

2 s

Question 48

A 2 kg object is moving at a constant speed of 5 m/s. What is the work done by the net force acting on the object?

Accepted Answer

0 J

Answer

50 J

Answer

10 J

Answer

25 J

Question 49

A spring with a spring constant of 100 N/m is stretched by 0.2 m. What is the potential energy stored in the spring?

Accepted Answer

2 J

Answer

1 J

Answer

4 J

Answer

10 J

Question 50

A 10 kg box is pushed across a rough horizontal floor by a constant force of 50 N. The coefficient of kinetic friction between the box and the floor is 0.3. What is the net work done on the box if it moves a distance of 5 m? (Take g = 10 m/s²)

Accepted Answer

100 J

Answer

200 J

Answer

150 J

Answer

50 J

Question 51

A particle is projected vertically upwards with a speed of 20 m/s. What is the maximum height reached by the particle? (Take g = 10 m/s²)

Accepted Answer

20 m

Answer

10 m

Answer

5 m

Answer

40 m

Question 52

A car of mass 1000 kg is travelling at a constant speed of 20 m/s. The brakes are applied, and the car comes to rest in a distance of 50 m. What is the magnitude of the braking force?

Accepted Answer

4000 N

Answer

1000 N

Answer

2000 N

Answer

8000 N

Question 53

A ball of mass 0.5 kg is thrown vertically upwards with an initial velocity of 10 m/s. What is the potential energy of the ball at its highest point? (Take g = 10 m/s²)

Accepted Answer

25 J

Answer

50 J

Answer

5 J

Answer

10 J

Question 54

A body of mass 2 kg is moving with a velocity of 4 m/s. What is the kinetic energy of the body?

Accepted Answer

16 J

Answer

8 J

Answer

4 J

Answer

32 J

Question 55

A 5 kg object is placed on a horizontal surface. The coefficient of static friction between the object and the surface is 0.4. What is the minimum force required to start the object moving?

Accepted Answer

19.6 N

Answer

49 N

Answer

29.4 N

Answer

9.8 N

Question 56

A force of 10 N acts on a body of mass 2 kg for 5 seconds. What is the change in momentum of the body?

Accepted Answer

50 kg m/s

Answer

10 kg m/s

Answer

20 kg m/s

Answer

25 kg m/s

Question 57

A particle is moving in a circular path of radius 5 m with a constant speed of 10 m/s. What is the centripetal acceleration of the particle?

Accepted Answer

20 m/s²

Answer

10 m/s²

Answer

5 m/s²

Answer

40 m/s²

Question 58

A 10 kg mass is suspended from a spring with a spring constant of 200 N/m. What is the period of oscillation of the mass-spring system?

Accepted Answer

1 s

Answer

2 s

Answer

4 s

Answer

0.5 s

Question 59

A car of mass 1000 kg is travelling at a speed of 20 m/s. What is the kinetic energy of the car?

Accepted Answer

200,000 J

Answer

100,000 J

Answer

400,000 J

Answer

50,000 J

Question 60

A ball is thrown horizontally from a cliff with a speed of 10 m/s. If the cliff is 20 m high, how long does it take for the ball to hit the ground? (Take g = 10 m/s²)

Accepted Answer

2 s

Answer

4 s

Answer

1 s

Answer

3 s