Master Mechanics: Motion and Forces in Mathematics for Sixth Form College

Question 1

A spring is stretched by 10 cm from its equilibrium position. What is the potential energy stored in the spring if the spring constant is 100 N/m?

Accepted Answer

0.5 J

Answer

1 J

Answer

1.5 J

Answer

2 J

Question 2

A block of mass 2 kg is sliding down a slope inclined at an angle of 30° to the horizontal. What is the acceleration of the block down the slope?

Accepted Answer

2.45 m/s²

Answer

4.9 m/s²

Answer

9.8 m/s²

Answer

14.7 m/s²

Question 3

A force of 10 N acts on an object for a duration of 2 seconds. Determine the impulse experienced by the object.

Accepted Answer

20 Ns

Answer

5 Ns

Answer

10 Ns

Answer

40 Ns

Question 4

Identify the conservative force among the following:

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 5

Which unit is used to measure power?

Accepted Answer

Watt

Answer

Joule

Answer

Newton

Answer

Kilogram

Question 6

A particle is moving in a straight line with constant velocity. Which of the following graphs best represents the relationship between its displacement and time?

Accepted Answer

A straight line with positive slope

Answer

A straight line with negative slope

Answer

A parabola opening upwards

Answer

A parabola opening downwards

Question 7

A 10 N force is applied to a 2 kg mass. What acceleration does the force produce?

Accepted Answer

2 m/s²

Answer

5 m/s²

Answer

10 m/s²

Answer

20 m/s²

Question 8

Which of the following expressions represents the elastic potential energy stored in a spring with spring constant 'k' that is stretched by a distance 'x'?

Accepted Answer

kx²/2

Answer

kx

Answer

kx³

Answer

kx⁴

Question 9

Which of the following forces is conservative?

Accepted Answer

Gravity

Answer

Friction

Answer

Air resistance

Answer

Tension

Question 10

In the equation W = Fd cosθ, which represents the work done by a force on an object, what does θ represent?

Accepted Answer

The angle between the force and the displacement

Answer

The angle between the force and the normal to the displacement

Answer

The angle between the displacement and the horizontal

Answer

The angle between the force and the vertical

Question 11

A ball is thrown vertically upwards with an initial velocity of 20 m/s. What maximum height is reached by the ball?

Accepted Answer

30 m

Answer

10 m

Answer

20 m

Answer

40 m

Question 12

A particle moves in a straight line with a constant velocity of 10 m/s for 5 seconds. Calculate the displacement of the particle.

Accepted Answer

25 m

Answer

50 m

Answer

10 m

Answer

15 m

Question 13

A force of 10 N acts on a mass of 2 kg. Calculate the acceleration produced in the mass.

Accepted Answer

2 m/s²

Answer

5 m/s²

Answer

10 m/s²

Answer

0.2 m/s²

Question 14

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Time

Answer

Temperature

Answer

Mass

Question 15

A car travels in a straight line with a constant speed of 20 m/s. What is the distance travelled in 5 seconds?

Accepted Answer

100 m

Answer

50 m

Answer

20 m

Answer

1 km

Question 16

A block of mass 5 kg is sliding on a rough surface with a coefficient of kinetic friction of 0.2. Determine the force of friction acting on the block.

Accepted Answer

2 N

Answer

1 N

Answer

5 N

Answer

10 N

Question 17

Which of the following is the unit of energy?

Accepted Answer

Joule

Answer

Newton

Answer

Metre

Answer

Second

Question 18

Which of the following types of friction opposes the motion of two surfaces in contact?

Accepted Answer

Kinetic friction

Answer

Static friction

Answer

Limiting friction

Answer

Rolling friction

Question 19

A wheel rotates at a constant angular velocity of 10 radians per second. What is its angular displacement after 5 seconds?

Accepted Answer

25 rad

Answer

10 rad

Answer

50 rad

Answer

100 rad

Question 20

Which of the following is a formula for the period of a simple pendulum?

Accepted Answer

T = 2π√(L/g)

Answer

T = 4π²√(L/g)

Answer

T = π²(L/g)

Answer

T = 2π(L/g)

Question 21

A particle moves in a circular path at a constant speed v. Which of the following is true about the acceleration of the particle?

Accepted Answer

It is always directed towards the center of the circle.

Answer

It is zero.

Answer

It is always directed away from the center of the circle.

Answer

It is always tangential to the circle.

Question 22

Which of the following describes the motion of an object in a spring-mass system undergoing simple harmonic motion?

Accepted Answer

Both 1 and 2 are correct.

Answer

The acceleration of the mass is proportional to the displacement of the mass.

Answer

The velocity of the mass is proportional to the displacement of the mass.

Answer

The energy of the system is constant.

Question 23

A horizontal force with a magnitude of 10 Newtons is applied to a 2-kilogram mass that is sitting on a frictionless surface. What is the acceleration of the mass?

Accepted Answer

5 m/s²

Answer

2.5 m/s²

Answer

10 m/s²

Answer

20 m/s²

Question 24

Which of the following forces is NOT considered conservative?

Accepted Answer

Frictional force

Answer

Gravitational force

Answer

Elastic force

Answer

Electrostatic force

Question 25

Which of the following is the unit of power in the International System of Units (SI)?

Accepted Answer

Watt

Answer

Joule

Answer

Newton

Answer

Meter

Question 26

A force of 50 N is exerted on an object with a mass of 10 kg for a duration of 10 s. Determine the impulse.

Accepted Answer

500 Ns

Answer

5 Ns

Answer

50 Ns

Answer

5000 Ns

Question 27

A particle moves in a circular path of radius 'R' with constant speed 'v'. Calculate the centripetal acceleration.

Accepted Answer

v² / R

Answer

v / R

Answer

R / v

Answer

R / v²

Question 28

A vehicle travels at a speed of 30 m/s. Calculate the distance it covers in 10 seconds.

Accepted Answer

300 m

Answer

3 m

Answer

0.3 m

Answer

0.03 m

Question 29

A force of 20 N is applied to a 5 kg object. Calculate the acceleration produced.

Accepted Answer

4 m/s²

Answer

1 m/s²

Answer

20 m/s²

Answer

100 m/s²

Question 30

A car travels 100 km in 2 hours. Calculate its average velocity.

Accepted Answer

50 km/h

Answer

25 km/h

Answer

100 km/h

Answer

200 km/h

Question 31

Which of the following statements is Newton's first law of motion?

Accepted Answer

An object at rest stays at rest, and an object in motion stays in motion at constant velocity unless acted on by an unbalanced force.

Answer

The acceleration of an object is directly proportional to the net force acting on it.

Answer

For every action, there is an equal and opposite reaction.

Question 32

Which of the following is a unit of energy?

Accepted Answer

Joule

Answer

Newton

Answer

Metre

Answer

Second

Question 33

A body of mass 2 kg is dropped from a height of 20 m. Determine its kinetic energy just before it hits the ground, considering the conservation of mechanical energy.

Accepted Answer

392 J

Answer

40 J

Answer

196 J

Answer

784 J

Question 34

Which of the following physical quantities is a vector?

Accepted Answer

Acceleration

Answer

Speed

Answer

Temperature

Answer

Mass

Question 35

Which condition must be satisfied for a system to be considered in equilibrium?

Accepted Answer

Both the net force and the net torque acting on the system are zero.

Answer

The net force acting on the system is zero.

Answer

The net torque acting on the system is zero.

Answer

Neither the net force nor the net torque acting on the system is zero.

Question 36

Identify the example of a non-conservative force.

Accepted Answer

Frictional force

Answer

Gravitational force

Answer

Tension force

Answer

Elastic force

Question 37

A rigid object experiences a torque of 10 Newton meters. If its moment of inertia is 5 kilogram meters squared, what is its angular acceleration?

Accepted Answer

2 rad/s²

Answer

5 rad/s²

Answer

10 rad/s²

Answer

20 rad/s²

Question 38

A particle with a mass of (m kg) moves in a circular path with a radius of (r m) at a tangential velocity of (v m/s). Calculate the centripetal force acting on the particle.

Accepted Answer

(mv^2/r)

Answer

(mr^2/v)

Answer

(mv/r)

Question 39

An object is moving with unchanging velocity. Which of the following forces is it experiencing?

Accepted Answer

Zero force

Answer

Force in the direction of motion

Answer

Force opposing the direction of motion

Answer

Force perpendicular to the direction of motion

Question 40

Classify the following quantity: Mass

Accepted Answer

Scalar quantity

Answer

Velocity

Answer

Displacement

Answer

Vector quantity

Question 41

A particle is moving in a circular path with constant speed. Its acceleration:

Accepted Answer

Is centripetal and perpendicular to its velocity

Answer

Is centrifugal and parallel to its velocity

Answer

Is centripetal and parallel to its velocity

Answer

Is centrifugal and perpendicular to its velocity

Question 42

Work done by a force acting on an object is zero when:

Accepted Answer

The force is perpendicular to the displacement

Answer

The force is equal to the weight of the object

Answer

The object is moving with constant velocity

Answer

The force is parallel to the displacement

Question 43

Which of the following is NOT a form of mechanical energy?

Accepted Answer

Heat

Answer

Potential energy

Answer

Kinetic energy

Answer

Elastic energy

Question 44

A ball is dropped from a height of 10 m. Its velocity when it reaches the ground is:

Accepted Answer

v = √(2gh)

Answer

v = 2gh

Answer

v = gh

Answer

v = (1/2)gh

Question 45

Which force is conservative?

Accepted Answer

Gravitational force

Answer

Frictional force

Answer

Tension force

Answer

Normal force

Question 46

An object moves with a constant velocity of 10 m/s. Calculate the distance it travels in 5 seconds.

Accepted Answer

50 m

Answer

10 m

Answer

100 m

Answer

25 m

Question 47

A 5 kg object moves at a constant velocity of 10 m/s. Determine the net force acting on the object.

Accepted Answer

0 N

Answer

10 N

Answer

50 N

Answer

5 N

Question 48

A spring with a spring constant of 100 N/m is stretched 0.2 meters. Calculate the elastic potential energy stored in the spring.

Accepted Answer

2 J

Answer

10 J

Answer

20 J

Answer

0.4 J

Question 49

Two objects of identical mass collide head-on with equal and opposite velocities. Determine the total momentum of the system after the collision.

Accepted Answer

0 kg·m/s

Answer

Cannot be determined without knowing the velocities

Answer

Equal to the momentum of one object before collision

Answer

Double the momentum of one object before collision

Question 50

A box is pulled across a horizontal floor with a force of 50 N. The coefficient of friction between the box and the floor is 0.2. What is the frictional force acting on the box?

Accepted Answer

10 N

Answer

50 N

Answer

100 N

Answer

25 N

Question 51

A car with a mass of 1000 kg is moving 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 52

A 5 kg object is lifted vertically by 2 meters. How much work is done against gravity? (Take g = 10 m/s²)

Accepted Answer

100 J

Answer

200 J

Answer

50 J

Answer

25 J

Question 53

A ball is thrown horizontally from a cliff with an initial speed of 15 m/s. If the ball takes 2 seconds to reach the ground, what is the horizontal distance traveled by the ball?

Accepted Answer

30 m

Answer

15 m

Answer

60 m

Answer

45 m

Question 54

A 10 kg object is moving at a constant velocity of 5 m/s. What is the net force acting on the object?

Accepted Answer

0 N

Answer

10 N

Answer

5 N

Answer

50 N

Question 55

A car traveling at a constant speed of 20 m/s goes around a bend with a radius of 50 meters. What is the centripetal acceleration of the car?

Accepted Answer

8 m/s²

Answer

2 m/s²

Answer

16 m/s²

Answer

4 m/s²

Question 56

A 10 kg box is pushed along a horizontal surface with a force of 20 N. The frictional force acting on the box is 5 N. What is the net force acting on the box?

Accepted Answer

15 N

Answer

20 N

Answer

5 N

Answer

25 N

Question 57

A box is pulled across a rough horizontal surface at a constant speed. Which statement is true about the forces acting on the box?

Accepted Answer

The applied force is equal and opposite to the frictional force.

Answer

The applied force is greater than the frictional force.

Answer

The applied force is less than the frictional force.

Question 58

A ball is thrown vertically upwards. At its highest point, what type of energy does the ball possess?

Accepted Answer

Potential energy

Answer

Both potential and kinetic energy

Answer

Neither potential nor kinetic energy

Answer

Kinetic energy

Question 59

A car accelerates uniformly from rest to a speed of 20 m/s over 5 seconds. What is the acceleration of the car?

Accepted Answer

4 m/s²

Answer

2 m/s²

Answer

1 m/s²

Answer

100 m/s²

Question 60

A 5 kg object is acted upon by a force of 20 N. What is the acceleration of the object?

Accepted Answer

4 m/s²

Answer

1 m/s²

Answer

25 m/s²

Answer

100 m/s²

Question 61

A 10 kg box is pulled across a horizontal surface by a force of 50 N. The coefficient of kinetic friction between the box and the surface is 0.2. What is the acceleration of the box?

Accepted Answer

3 m/s²

Answer

5 m/s²

Answer

1 m/s²

Answer

10 m/s²

Question 62

A 1 kg ball is dropped from a height of 10 m. What is the kinetic energy of the ball just before it hits the ground? (Assume g = 10 m/s²)

Accepted Answer

100 J

Answer

50 J

Answer

20 J

Answer

10 J

Question 63

What is the work done when a force of 20 N moves an object through a displacement of 5 m?

Accepted Answer

100 J

Answer

50 J

Answer

150 J

Question 64

A ball is dropped from a height of 10 m. What is its kinetic energy just before it hits the ground?

Accepted Answer

100 J

Answer

50 J

Answer

150 J