List of physical constants (to use for all questions of this test)

Speed of sound in air: 340 m s^-1
Speed of light in a vacuum: 3.00×10⁸ m s^-1
Acceleration due to gravity: 9.80 m s^-2
Specific heat capacity of water: 4.19×10³ J kg^-1 °C^-1

An equation for the position x of an object at a time t is given by: x = bt ³ + ct ⁴, where b and c are two constants. The dimensions of b and c are, respectively:

T³, T⁴

1/T³, 1/T⁴

L/T³, L/T⁴

LT³, LT⁴

L²T³, L²T⁴

A force acting on an object along the x-axis varies with position as F = 6.0x², where F is in newtons and x is in metres. What is the work done by the force when the object moves from x = 1.0 m to x = 3.0 m?

52 J

54 J

48 J

108 J

60 J

Two planar vectors a and b are given by a = i – 2j and b = 3i + j, where i and j are perpendicular unit vectors. The dot (scalar) product of these two vectors is:

1.00 units

2.00 units

3.20 units

1.50 units

undetermined

A car accelerates at a constant rate from rest to a speed of 100 km/hr in 8.00 s. What is its speed after the first 5.00 s of the acceleration?

34.7 m s^-1

44.4 m s^-1

28.7 m s^-1

17.4 m s^-1

800 m s^-1

A car starts with a speed of 5 m s⁻¹ and accelerates uniformly at 2 m s⁻² for 6 s. It then travels at the speed it has reached for a further 4 s. What is the total displacement of the car during the 10 s interval?

10 m

12 m

66 m

134 m

188 m

A rock is thrown vertically upwards with an initial velocity of 24.5 m s^-1. What maximum height will the rock reach?

9.80 m

19.6 m

24.5 m

30.6 m

240 m

A car of mass 2.00×10³ kg moving at 30.0 m/s is suddenly decelerated by a constant force of 1.00×10⁴ N. How far does the car travel before stopping?

45.0 m

90.0 m

135 m

150 m

180 m

The mass of a simple pendulum is moved by an angle so that it is vertically displaced by a height of 1.00 m. The mass is then released from rest. What is the speed of the mass when it passes through the equilibrium position?

0 m s^-1

1.00 m s^-1

3.13 m s^-1

4.43 m s^-1

19.6 m s^-1

A mass on a spring oscillates with simple harmonic motion of amplitude A and period 1.20 s. What is the shortest time taken for the mass to move from the position x = A to the position x = A/2?

0.100 s

0.300 s

0.150 s

0.400 s

0.200 s

When an ideal spring is compressed by 12.0 cm from equilibrium, the potential energy stored in it is 72.0 J. What is the spring constant?

6.00 N m^-1

864 N m^-1

1.20x10³ N m^-1

5.00x10³ N m^-1

1.00x10⁴ N m^-1

A piano string emits a sound wave of frequency 440 Hz. What is the wavelength of this sound wave?

0.773 m

6.82×10⁵ m

1.29 m

0.850 m

1.49×10⁵ m

A mass of 0.250 kg of hot water is initially at a temperature of 35ºC. How much energy is required to bring the water to its boiling point at 100ºC?

16.2 J

6.81×10⁴ J

6.81×10⁷ J

1.05×10⁵ J

8.61×10⁴ J

Consider the following resistances, where R1 = 5 Ω, R2 = 10 Ω and R3 = 10 Ω.

What is the equivalent resistance between the points a and b?

5 Ω

10 Ω

25 Ω

105 Ω

0 Ω

Three devices are connected to a 240 V house circuit and draw currents of 1.0 A, 2.0 A and 3.0 A, respectively. All three devices operate simultaneously for 4.0 hours. Electricity costs 30 p per kWh. What is the cost of operating the three devices for the 4.0-hour period?

£0.36

£0.66

£0.89

£1.73

£2.05

A conducting rod of length 0.50 m slides without friction on two parallel conducting rails. The rails are connected by a resistor of resistance 2.0 Ω, forming a complete circuit. The rod and rails have negligible resistance. The entire arrangement is in a uniform magnetic field of flux density 0.80 T directed into the page. The rod is pulled to the right at a constant speed of 10 m s⁻¹. What is the rate at which mechanical work is done in pulling the rod?

8 W

10 W

12 W

14 W

16 W

In the image above, a negatively charged particle (– Q) is moving to the right, directly above a wire having a current flowing to the right, as shown in the figure. In which direction is the magnetic force exerted on the particle?

into the page

out of the page

downward

upward

the magnetic force is zero

A capacitor of capacitance C, initially charged to Q₀, is connected in parallel to two uncharged capacitors of capacitances C/2 and C/3. After the system reaches equilibrium, what is the total electrical energy stored in the system of capacitors?

Q₀²/2C

5Q₀²/6C

3Q₀²/11C

6Q₀²/11C

Q₀²/C

In the diagram shown below, a ray of monochromatic light travels from a material X with refractive index n1 = 1.63 to a material Y with refractive index n2 = 1.57 and grazes the interface with a material Z of an unknown index of refraction n3 at 90 º. If the angle of incidence of the ray is θ1 = 32.1º, 

what is the unknown index of refraction n₃ of the material Z?

1.23

1.94

1.54

1.75

1.31

A uniform thin rod of length L and mass M rotates about a fixed axis perpendicular to the rod. The axis initially passes through the centre of the rod. The rod is then stopped, and the rotation axis is moved to one end of the rod. The same angular speed ω is applied again. Which statement correctly compares the rotational kinetic energy of the rod in the two cases?

The kinetic energy is unchanged because the mass and angular speed are the same.

The kinetic energy is four times as large when rotating about the end, because the moment of inertia about the end is four times that about the centre.

The kinetic energy is twice as large when rotating about the end because the moment of inertia doubles.

The kinetic energy is larger when rotating about the end because the moment of inertia increases, but the exact factor cannot be determined without knowing the angular acceleration.

The kinetic energy is smaller when rotating about the end because the rod experiences greater centripetal forces that oppose the motion.

A pendulum of length l and mass m undergoes simple harmonic motion. At an angle θ, the instantaneous speed is v. Which equation represents the tension force T acting on the mass?

mg cosθ

m(gcosθ − (v²/l))

mg sinθ

m(gsinθ − (v²/l))

m(gcosθ + (v²/l))

If the net torque on an object is zero then :

the forces on it also add up to zero

the object could be accelerating linearly but cannot be turning

the object cannot be turning and cannot be accelerating

the object could be accelerating linearly and it could be turning

the object is at rest

In a particular nuclear reaction, electrons and alpha particles are emitted, with the electrons having twice the speed of the alpha particles. An alpha particle is made of two neutrons and two protons. It is known that m_proton ≈ m_neutron ≈ 1,836 m_electron.

The ratio of the de Broglie wavelength of an electron over the de Broglie wavelength of an alpha particle is most closely equal to:

6,344

4,366

7,344

3,672

11,016

Monochromatic light of wavelength λ = 400 nm passes through a double slit, and an interference pattern is observed on a distant screen. If the distance d between the slits is 0.150 mm, what is the approximate angle of the third order maximum (bright fringe) that is observed on the screen?

0.458º

0.225º

0.115º

0.201º

0.405º

A radioactive substance decays exponentially. After 3 hours, only 20% of the original sample remains. How much of the original sample will remain after a total of 8 hours?

1.07%

1.37%

3.09%

6.07%

10.10%

An object of initial speed v = 13.2 ms^-1 decelerates uniformly on a horizontal plane. The coefficient of kinetic friction between the object and the plane is 0.360. What approximate distance will the object travel until it comes to rest?

26.3 m

49.4 m

19.5 m

32.9 m

24.7 m

Two springs of constants k₁ = 40.0 N/m and k₂ = 20.0 N/m are connected in parallel, as shown in the diagram. What approximate extension x is required by the force F if the system of springs is to store an amount of elastic potential energy equal to 3.36 J?

0.923 m

0.335 m

0.622 m

0.434 m

0.526 m

An object rotates at a constant speed v = 6π ms^-1 in a horizontal circle of radius 3.00 m. If the centripetal force acting on the object is 3π²/9 N, what is its angular momentum equal to?

3π kgm²s^-1

2π kgm²s^-1

π/2 kgm²s^-1

π/3 kgm²s^-1

π kgm²s^-1

A mass moves under the influence of a conservative force along an open path. At some point along this path, the potential energy U of the mass equals 3 times its kinetic energy K and the difference between U and K equals 40 J. What is the Mechanical Energy of the mass equal to?

20 J

60 J

40 J

80 J

100 J

A 2.30 kg object travelling at 6.80 m s^-1 to the right collides head-on with a 4.50 kg object travelling to the left at 2.60 m s^-1. If the masses stick together after the collision, and move to the right, what is their common speed after the collision?

0.412 ms^-1 

0.579 ms^-1 

0.687 ms^-1

0.787 ms^-1

0.839 ms^-1

A particle has a mass-to-charge ratio m/q equal to 200 kg/C and enters a uniform magnetic field of magnitude B = 4.00 T with a velocity v perpendicular to the field lines. The period of rotation T of the particle inside the magnetic field is equal to:

40 π s

200 π s

100 π s

40 π/3 s

300 π s