Further Mechanics 2: Master Momentum, Impulse, and Torque

Question 1

A car of mass 1000 kg is traveling at a velocity of 10 m/s. Its engine exerts a constant force of 2000 N on the car for 5 seconds. Calculate the car's final velocity.

Accepted Answer

12 m/s

Answer

15 m/s

Answer

8 m/s

Answer

10 m/s

Question 2

A torque of 5 Nm is applied to a wheel of radius 0.2 m. Calculate the angular acceleration of the wheel.

Accepted Answer

25 rad/s²

Answer

10 rad/s²

Answer

50 rad/s²

Answer

100 rad/s²

Question 3

A ball is dropped from a height of 20 m. What is its velocity when it hits the ground?

Accepted Answer

30 m/s

Answer

10 m/s

Answer

20 m/s

Answer

40 m/s

Question 4

A car with a mass of 1000 kilograms is traveling at a velocity of 20 meters per second. Determine its kinetic energy.

Accepted Answer

200 kJ

Answer

100 kJ

Answer

50 kJ

Answer

150 kJ

Question 5

Which of the following is a vector quantity?

Accepted Answer

Momentum

Answer

Distance

Answer

Mass

Answer

Energy

Question 6

A particle moves in a straight line. Its velocity v at time t is given by v = at + b, where a and b are constants. What is the momentum of the particle at time t?

Accepted Answer

mat

Answer

ma(t + b)

Answer

mbt

Answer

constant

Question 7

A force F acts on a particle of mass m for a duration t. What is the impulse imparted to the particle?

Accepted Answer

Ft

Answer

F/t

Answer

Ft/m

Answer

mFt

Question 8

A rocket engine exerts a constant thrust F on a rocket of mass m. The rocket starts from rest and moves vertically upwards. What is the acceleration of the rocket?

Accepted Answer

F/m

Answer

F/mg

Answer

mg/F

Answer

gm/F

Question 9

A body is in equilibrium under the action of three forces. State the condition for equilibrium.

Accepted Answer

The forces are equal in magnitude and opposite in direction

Answer

The forces are equal in magnitude and parallel

Answer

The forces are equal in magnitude and perpendicular

Answer

The forces are equal in magnitude and non-parallel

Question 10

A body of mass 'm' is projected vertically upwards with velocity 'u'. If the air exerts a constant resistance of magnitude 'R' on the body, the maximum height reached by the body is:

Accepted Answer

u²/2(g-R/m)

Answer

u²/2g

Answer

u²/2R

Answer

u²/2(g+R/m)

Question 11

A rigid body is rotating about a fixed axis. The angular momentum of the body is conserved if:

Accepted Answer

The net torque acting on the body is zero

Answer

The body is not acted upon by any external forces

Answer

The body is in equilibrium

Answer

The body is moving with constant velocity

Question 12

A particle of mass 'm' is moving in a circular path of radius 'r' with constant speed 'v'. The force acting on the particle is:

Accepted Answer

mv²/r towards the centre

Answer

mv²/r away from the centre

Answer

Zero

Answer

mg downwards

Question 13

A particle of mass 'm' is moving in a circle of radius 'r' with constant speed 'v'. The time period of the motion is:

Accepted Answer

2πr/v

Answer

πr/v

Answer

π²/rv

Answer

2π²/rv

Question 14

A force of 10 N is applied to an object with a mass of 5 kg for 2 seconds. Determine the impulse applied to the object.

Accepted Answer

20 Ns

Answer

5 Ns

Answer

10 Ns

Answer

50 Ns

Question 15

A torque of 20 Nm is applied to a wheel with a radius of 0.5 m. Calculate the wheel's moment of inertia.

Accepted Answer

4 kgm²

Answer

2 kgm²

Answer

10 kgm²

Answer

20 kgm²

Question 16

A body is launched vertically upward with a velocity of 20 m/s. Determine the maximum height reached by the body.

Accepted Answer

30 m

Answer

10 m

Answer

20 m

Answer

40 m

Question 17

An elastic collision between two bodies is characterized by the:

Accepted Answer

Conservation of both total kinetic energy and total momentum

Answer

Conservation of total kinetic energy

Answer

Conservation of total momentum

Answer

Loss of total kinetic energy

Question 18

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Answer

Displacement

Answer

Velocity

Answer

Force

Question 19

In the International System of Units (SI), the unit of moment of inertia is:

Accepted Answer

kilogram meter squared

Answer

kilogram

Answer

newton meter

Answer

joule

Question 20

A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of a point on the rim of the wheel?

Accepted Answer

ωR

Answer

ωR/2

Answer

2ωR

Answer

ωR/4

Question 21

A particle of mass m is moving in a circular path of radius r with a constant speed v. What is the magnitude of the angular momentum of the particle?

Accepted Answer

mrv

Answer

0

Answer

2mrv

Answer

3mrv

Question 22

A force of 10 N is applied to a stationary object of mass 2 kg for 2 seconds. Calculate the final velocity of the object (Impulse = change in momentum).

Accepted Answer

5 m/s (10 N * 2 s / 2 kg)

Answer

10 m/s (10 N * 2 s / 2 kg)

Answer

20 m/s (10 N * 2 s / 2 kg)

Question 23

A force of 10 N is applied at a perpendicular distance of 0.5 m from a pivot to a body. What is the torque produced?

Accepted Answer

5 Nm (10 N * 0.5 m)

Answer

10 Nm (10 N * 1 m)

Answer

15 Nm (10 N * 1.5 m)

Question 24

A body of mass 5 kg has a kinetic energy of 25 J. Determine the velocity of the body.

Accepted Answer

7.5 m/s (sqrt(2 * 25 J / 5 kg))

Answer

5 m/s (sqrt(2 * 25 J / 5 kg))

Answer

10 m/s (sqrt(2 * 25 J / 5 kg))

Question 25

A car of mass 1000 kg is travelling at a speed of 20 m/s. The brakes are applied, providing a constant deceleration of 4 m/s^2. What is the work done by the brakes to bring the car to a stop?

Accepted Answer

160 kJ

Answer

20 kJ

Answer

40 kJ

Answer

80 kJ

Question 26

A particle of mass m is moving with speed v along a straight line. A constant force F is applied in the direction of motion for a time t. Calculate the work done by the force.

Accepted Answer

Ft

Answer

mvt

Answer

1/2 mvt^2

Answer

1/2 Ft^2

Question 27

A particle of mass m is projected vertically upward with an initial velocity u. Determine the maximum height reached by the particle.

Accepted Answer

u^2/2g

Answer

ug/2

Answer

2u^2/g

Answer

2ug

Question 28

The SI unit of impulse is:

Accepted Answer

newton second

Answer

kilogram meter per second

Answer

kilogram meter per second squared

Answer

newton

Question 29

A ball with a mass of 0.5 kg is traveling at a velocity of 10 m/s. What is its momentum?

Accepted Answer

2.5 kg m/s

Answer

5 kg m/s

Answer

10 kg m/s

Answer

0.25 kg m/s

Question 30

Newton's third law of motion states that:

Accepted Answer

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

Answer

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

Answer

An object at rest will remain at rest unless acted upon by an unbalanced force.

Answer

The momentum of an isolated system remains constant.

Question 31

The impulse experienced by a body when a force of 10 N is applied for 5 seconds is:

Accepted Answer

20 Ns

Answer

10 Ns

Answer

50 Ns

Answer

100 Ns

Question 32

The SI unit of torque is:

Accepted Answer

newton meter

Answer

newton

Answer

kilogram meter per second

Answer

kilogram meter per second squared

Question 33

The principle of moments states that:

Accepted Answer

The sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point.

Answer

The torque produced by a force is equal to the product of the force and the lever arm.

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 34

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Temperature

Answer

Speed

Question 35

A projectile is launched vertically upward with an initial velocity of 20 m/s. What is the maximum height it will reach?

Accepted Answer

40 m

Answer

20 m

Answer

60 m

Answer

80 m

Question 36

A particle of mass m moves in a circle of radius r at a constant speed v. What is the magnitude of the resultant force acting on the particle?

Accepted Answer

mv²/r

Answer

mv²/2r

Answer

2mv²/r

Answer

zero

Question 37

An object of mass 5 kg slides down a frictionless inclined plane that makes an angle of 30° with the horizontal. What is the acceleration of the object?

Accepted Answer

19.6 m/s²

Answer

5 m/s²

Answer

9.8 m/s²

Answer

24.5 m/s²

Question 38

A car of mass 1000 kg travels at a speed of 20 m/s. What is the magnitude of the car's momentum?

Accepted Answer

2000 kg m/s

Answer

1000 kg m/s

Answer

5000 kg m/s

Answer

10000 kg m/s

Question 39

A constant force of 10 N acts on a body of mass 2 kg for a duration of 5 seconds. Calculate the change in momentum of the body:

Accepted Answer

50 Ns

Answer

10 Ns

Answer

20 Ns

Question 40

A system of two particles has a total linear momentum of zero. This implies that the particles:

Accepted Answer

Have equal and opposite momenta

Answer

Have the same momentum with the same direction

Answer

Have different momenta with the same direction

Question 41

A particle moves in a circle of radius r with a constant tangential speed v. The centripetal acceleration of the particle is:

Accepted Answer

v^2 / r

Answer

v / r

Answer

r * v

Answer

r / v

Question 42

A uniform rod of length 2 m and weight 10 N is pivoted at one end. A force of 5 N is applied perpendicular to the rod at a distance of 0.5 m from the pivot. Calculate the torque about the pivot.

Accepted Answer

2.5 Nm

Answer

10 Nm

Answer

5 Nm

Answer

15 Nm

Question 43

A wheel of radius 0.3 m is rotating about a fixed axis with an angular velocity of 20 rad/s. Calculate the linear velocity of a point on the rim of the wheel.

Accepted Answer

6 m/s

Answer

4 m/s

Answer

8 m/s

Question 44

A lever has a length of 1 m. A force of 20 N is applied to the lever at a distance of 0.5 m from the pivot point. A load of 80 N is applied at a distance of 0.25 m from the pivot point. Is the lever in equilibrium?

Accepted Answer

No

Answer

Yes, clockwise

Answer

Yes, anticlockwise

Question 45

A ball of mass m is projected horizontally with a velocity u. If the coefficient of restitution between the ball and the ground is e, calculate the velocity of the ball after the first bounce.

Accepted Answer

(1-e)u

Answer

eu

Answer

0

Answer

(e-1)u

Question 46

A body is in equilibrium under the action of three forces, F1, F2, and F3, which are concurrent. Which statement is true?

Accepted Answer

F1 + F2 = F3

Answer

F1 - F2 = F3

Answer

F1 / F2 = F3

Answer

F1 * F2 = F3

Question 47

A particle of mass m is moving with a velocity v. Calculate the momentum of the particle.

Accepted Answer

mv

Answer

m/v

Answer

v/m

Answer

m^2v

Question 48

A system of particles has a total momentum of zero. Which statement is true?

Accepted Answer

The system is either at rest or moving with a constant velocity.

Answer

The system is decelerating.

Answer

The system is accelerating.

Question 49

A torque of T is applied to a rigid body about an axis. Calculate the angular acceleration produced.

Accepted Answer

T/I

Answer

I^2/T

Answer

I/T

Answer

T^2/I

Question 50

A flywheel of moment of inertia I is rotating about its axis with an angular velocity ω. Calculate the kinetic energy of the flywheel.

Accepted Answer

1/2Iω^2

Answer

1/ω^2

Answer

Iω^2

Answer

Iω

Question 51

A body is acted upon by a force F which is always perpendicular to its velocity. Calculate the work done by the force.

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Question 52

A 1-meter long rod is pivoted at one end. A 5 N force is applied perpendicularly to the rod at a point 0.5 meters from the pivot. Calculate the torque acting on the rod.

Accepted Answer

2.5 Nm

Answer

1.25 Nm

Answer

5 Nm

Answer

3.75 Nm

Question 53

A 1 kg particle is launched vertically upwards with an initial velocity of 10 m/s. Determine the maximum height reached by the particle.

Accepted Answer

5 m

Answer

10 m

Answer

2.5 m

Answer

7.5 m

Question 54

A spring with a spring constant of 100 N/m is stretched by 0.1 meters. Calculate the potential energy stored in the spring.

Accepted Answer

0.5 J

Answer

0.25 J

Answer

2 J

Answer

1 J

Question 55

A 2 kg mass moving at 5 m/s collides head-on with a stationary 3 kg mass. They stick together after the collision. Calculate their combined velocity.

Accepted Answer

1.67 m/s

Answer

2.5 m/s

Answer

3.33 m/s

Question 56

A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. Determine the average power output of the car during this acceleration.

Accepted Answer

20 kW

Answer

100 kW

Answer

40 kW

Answer

10 kW

Question 57

A 0.5 kg ball is attached to a 0.8 m string and whirled in a horizontal circle at a speed of 10 m/s. Calculate the kinetic energy of the ball.

Accepted Answer

50 J

Answer

100 J

Answer

75 J

Answer

25 J

Question 58

A 2 kg body moving at 5 m/s collides head-on with a stationary 3 kg body. The coefficient of restitution is 0.5. Determine the velocity of the 2 kg body after the collision.

Accepted Answer

2.5 m/s

Answer

4.5 m/s

Answer

1.5 m/s

Answer

3.5 m/s

Question 59

A uniform 5 kg rod, 2 meters long, is pivoted at one end. A 10 N force is applied perpendicularly to the rod at a point 1 meter from the pivot. What is the angular acceleration of the rod?

Accepted Answer

25 rad/s²

Answer

37.5 rad/s²

Answer

12.5 rad/s²

Answer

50 rad/s²

Question 60

A projectile is launched at a 30° angle to the horizontal with an initial speed of 20 m/s. Calculate the maximum height reached by the projectile.

Accepted Answer

10 m

Answer

20 m

Answer

5 m

Answer

15 m

Question 61

A 1000 kg car travelling at 30 m/s brakes to a stop over a distance of 50 m. Calculate the coefficient of friction between the tires and the road.

Accepted Answer

0.36

Answer

0.27

Answer

0.54

Answer

0.45

Question 62

A satellite with a mass of 500 kg orbits Earth at a height of 6400 km above the Earth's surface.  What is the approximate orbital period of this satellite?

Accepted Answer

5.9 hours

Answer

3.9 hours

Answer

10.9 hours

Answer

7.9 hours

Question 63

A spring with a spring constant of 100 N/m is stretched 0.2 meters from its equilibrium position.  What is the potential energy stored in the spring?

Accepted Answer

2 J

Answer

1 J

Answer

4 J

Answer

3 J

Question 64

A uniform disc with a radius of 0.5 meters rolls without slipping at a speed of 5 m/s. What is the kinetic energy of the disc?

Accepted Answer

20.8 J

Answer

10.4 J

Answer

31.2 J

Answer

15.6 J