Physics Equations and Constants

What represents a physical quantity?

The relationship between the variables D and T is given by the equation $\frac{1}{T} = \frac{b}{\sqrt{D}} + c$ where b and c are constants. The unit of D is $m^2$ and the unit of T is s. What are the units of b and c?

A hollow cylinder, which is open at both ends, has a radius of (3.0 ± 0.1)cm and a length of (15.0 ± 0.1)cm. What is the value, with its absolute uncertainty, of the surface area of the cylinder?

A snooker ball of mass 0.20 kg has a collision so that its direction of movement changes by an angle of 90°, as shown. The ball has a speed of 0.40 ms¯¹ before the collision and a speed of 0.30 ms¯¹ after the collision. What is the magnitude of the change in momentum of the snooker ball?

A ball is kicked upwards at an angle of 45° to horizontal ground. After a short flight, the ball returns to the ground. It may be assumed that air resistance is negligible. What is never zero during the flight of the ball?

The graph shows the variation with time t of the displacement s of an object. Which graph represents the variation with time t of the acceleration a of the object?

Which expression defines force?

A ship of mass 8.4 × 107 kg is approaching a harbour with speed 16.4ms¯¹. By using reverse thrust it can maintain a constant total stopping force of 920 000 N. How long will it take to stop?

The velocity-time graphs of four different objects are shown. Which graph represents an object falling from rest through a long distance in the Earth's atmosphere?

Which statement about collisions is correct?

A satellite uses two thrusters to adjust its motion in space. Each thruster exerts a force of 40 N on the satellite. The line of action of each force is a perpendicular distance of 2.3m from the centre of gravity of the satellite. These two parallel forces act in opposite directions. What are the magnitudes of the torque and the resultant force acting on the satellite due to the two thrust forces?

The diagrams show two ways of hanging the same picture. In both cases, a string is attached to the same points on the picture and looped symmetrically over a nail in a wall. The forces shown are those that act on the nail. In diagram 1, the string loop is shorter than in diagram 2. Which information about the magnitude of the forces is correct?

A probe is used to monitor the quality of the water in the sea. The probe is suspended by a vertical string which is attached to a sphere. The stationary sphere floats in equilibrium on the surface of the sea, as shown. The sphere has a weight of 5.00 N. The probe and string have a combined weight of 2.00 N. The density of the seawater is 1.03 × 103kgm¯³. The upthrust acting on the probe and thread is negligible. What is the volume of the sphere below the surface of the sea?

What is the centre of gravity of an object?

A system with an efficiency of 74% wastes 230W of power. What is the useful output power of the system?

A projectile of mass 0.25 kg is at a height of 30m above horizontal ground and travelling at a speed of 15ms¯¹. A short time later, it is at a height of 35m above the horizontal ground and travelling at a speed of 5.0 ms¯¹. How much work is done against air resistance during this time?

A spring has an unstretched length of 4.50cm. The spring is fixed at one end and a force of 35.0 N is applied to the other end so that the spring extends. The spring obeys Hooke's law and has a spring constant of 420 Nm¯¹. What is the strain of the extended spring?

A wire is fixed at one end and extended by a force that is applied to the other end. The force is slowly increased from zero and then slowly decreased back to zero. The force-extension graph for the wire is shown. The graph line for the wire being loaded is the same as the graph line for the wire being unloaded. Which statement describes the deformation of the wire?

In a progressive water wave, two particles, P and Q, on the surface of the water, are a fixed horizontal distance apart. P and Q oscillate vertically. At time t = 0, the wave is as shown. Which graph best represents the variation with time t of the phase difference φ between the oscillation of the water particle P and the oscillation of the water particle Q?

Which statement about longitudinal waves and transverse waves is not correct?

An observer hears a sound wave emitted from a moving source. The observed frequency is less than the frequency of sound emitted from the source. What could be the reason for this?

What is the approximate range of frequencies of electromagnetic radiation visible to the human eye?

A beam of vertically polarised light is incident normally on a polarising filter. The filter can be rotated so that it is always in a plane perpendicular to the beam. The transmission axis of the filter is initially vertical. The filter is first rotated clockwise by an angle of 30° so that the transmitted light waves have intensity $I_{30}$. The filter is then rotated clockwise by a further angle of 30°. What is the new intensity of the transmitted light waves?

A musical instrument is made using a long tube with a mouthpiece at one end. The other end is open and flared, as shown. A musician maintains stationary sound waves with a node at the mouthpiece and an antinode at the other end. The lowest frequency of sound that the instrument can produce is 92 Hz. Which different frequencies of sound can be produced by the instrument?

Two waves of equal frequency and amplitude are travelling in opposite directions along a stretched string. When they meet, they form a stationary wave with three nodes and two antinodes. The frequency of both waves is doubled and a new stationary wave is formed. How many antinodes are there in the new stationary wave?

A transmitting mast sends out microwaves of wavelength 1.5cm and radio waves of wavelength 1.5 km. A receiving aerial behind a mountain can detect the radio waves but not the microwaves. What is the reason for this?

Waves are emitted from two coherent sources. Which statement about the waves must be correct?

The diagram shows a screen that is a distance L from a diffraction grating. The grating has a total number of N lines. Any two adjacent lines are a distance d apart. A beam of parallel light of wavelength λ is incident normally on the grating. Which quantities affect the distance between the first-order diffraction maxima on the screen?

A wire carries a current of 0.10µA. The potential difference across the wire is 10 mV. How much energy is dissipated by the wire in a time of 10 s?

What is the definition of the potential difference across an electrical component?

A snooker ball of mass 0.20 kg has a collision so that its direction of movement changes by an angle of 90°, as shown. The ball has a speed of 0.40 $ms^{-1}$ before the collision and a speed of 0.30 $ms^{-1}$ after the collision. What is the magnitude of the change in momentum of the snooker ball?

The graph shows the variation with time t of the displacements s of an object. [graph of displacement vs time] Which graph represents the variation with time t of the acceleration a of the object?

A ship of mass 8.4 × $10^7$ kg is approaching a harbor with speed 16.4$ms^{-1}$. By using reverse thrust it can maintain a constant total stopping force of 920 000 N. How long will it take to stop?

The velocity-time graphs of four different objects are shown. [four velocity time graphs]. Which graph represents an object falling from rest through a long distance in the Earth's atmosphere?

A satellite uses two thrusters to adjust its motion in space. Each thruster exerts a force of 40 N on the satellite. The line of action of each force is a perpendicular distance of 2.3m from the centre of gravity of the satellite. These two parallel forces act in opposite directions. [diagram of satellite]. What are the magnitudes of the torque and the resultant force acting on the satellite due to the two thrust forces?

The diagrams show two ways of hanging the same picture. [two diagrams of picture hanging systems]. In both cases, a string is attached to the same points on the picture and looped symmetrically over a nail in a wall. The forces shown are those that act on the nail. In diagram 1, the string loop is shorter than in diagram 2. Which information about the magnitude of the forces is correct?

An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r and density p. [hemisphere diagram]. The volume of a sphere is $\frac{4}{3}πr³$. Which average pressure does the object exert on the table?

A probe is used to monitor the quality of the water in the sea. The probe is suspended by a vertical string which is attached to a sphere. The stationary sphere floats in equilibrium on the surface of the sea, as shown. [diagram of probe]. The sphere has a weight of 5.00 N. The probe and string have a combined weight of 2.00 N. The density of the seawater is 1.03 × 103kgm⁻³. The upthrust acting on the probe and thread is negligible. What is the volume of the sphere below the surface of the sea?

A projectile of mass 0.25 kg is at a height of 30m above horizontal ground and travelling at a speed of 15ms⁻¹. A short time later, it is at a height of 35m above the horizontal ground and travelling at a speed of 5.0 ms⁻¹. How much work is done against air resistance during this time?

A spring has an unstretched length of 4.50cm. The spring is fixed at one end and a force of 35.0 N is applied to the other end so that the spring extends. The spring obeys Hooke's law and has a spring constant of 420 $Nm^{-1}$. What is the strain of the extended spring?

A wire is fixed at one end and extended by a force that is applied to the other end. The force is slowly increased from zero and then slowly decreased back to zero. The force-extension graph for the wire is shown. [Force Extension Graph]. The graph line for the wire being loaded is the same as the graph line for the wire being unloaded. Which statement describes the deformation of the wire?

In a progressive water wave, two particles, P and Q, on the surface of the water, are a fixed horizontal distance apart. P and Q oscillate vertically. At time t = 0, the wave is as shown. [Wave Diagram]. Which graph best represents the variation with time t of the phase difference between the oscillation of the water particle P and the oscillation of the water particle Q?

A beam of vertically polarised light is incident normally on a polarising filter. The filter can be rotated so that it is always in a plane perpendicular to the beam. The transmission axis of the filter is initially vertical. [Vertically Polarised light diagram] The filter is first rotated clockwise by an angle of 30° so that the transmitted light waves have intensity $I_{30}$. The filter is then rotated clockwise by a further angle of 30°. What is the new intensity of the transmitted light waves?

A musical instrument is made using a long tube with a mouthpiece at one end. The other end is open and flared, as shown. [Musical instrument diagram] A musician maintains stationary sound waves with a node at the mouthpiece and an antinode at the other end. The lowest frequency of sound that the instrument can produce is 92 Hz. Which different frequencies of sound can be produced by the instrument?

A transmitting mast sends out microwaves of wavelength 1.5cm and radio waves of wavelength 1.5 km. [Transmitting Mast diagram] A receiving aerial behind a mountain can detect the radio waves but not the microwaves. What is the reason for this?

The diagram shows a screen that is a distance L from a diffraction grating. The grating has a total number of N lines. Any two adjacent lines are a distance d apart. A beam of parallel light of wavelength is incident normally on the grating. [Diffraction grating diagram]. Which quantities affect the distance between the first-order diffraction maxima on the screen?

Which graph represents the way the current I through a filament lamp varies with the potential difference V across it?

The table shows the properties of two different wires, P and Q. [tabular diagram]. Wire P has a cross-section of diameter d. What is the diameter of the cross-section of wire Q?

A cell has a constant electromotive force. A variable resistor is connected between the terminals of the cell. The resistance of the variable resistor is decreased. Which statement about the change of the cell's terminal potential difference (p.d.) is correct?

Kirchhoff's two laws for electric circuits can be derived by using conservation laws. On which conservation laws do Kirchhoff's laws depend?

A battery of electromotive force (e.m.f.) 10V and internal resistance r is connected to three resistors of resistances R, 2.0Ω and 15Ω, as shown. [Circuit Diagram.] A current of 0.45 A is in the resistor of resistance 2.0Ω and a current of 0.48 A is in the resistor of resistance 15Ω. What are the values of r and R?

A battery of negligible internal resistance is connected in series with a thermistor and a fixed resistor of resistance 12.0kΩ, as shown. The table shows the resistance of the thermistor at two different temperatures. [circuit and table]. The potential difference $V_{out}$ across the fixed resistor is 4.50V when the thermistor is at a temperature of 20.0°C. What is $V_{out}$ when the thermistor is at a temperature of 50.0°C?

What is a conclusion from the alpha-particle scattering experiment?

Americium-241 is a radioactive nuclide used in smoke detectors. It undergoes a-decay to form nuclide X. This decay may be represented by the equation shown. [nuclear equation] What are the values of A and Z?

A top quark has a charge of +⅔ e, where e is the elementary charge. What is the charge of an anti top quark?

The relationship between the variables D and T is given by the equation $1/T = b/\sqrt{D} + c$ where b and c are constants. The unit of D is $m^2$ and the unit of T is s. What are the units of b and c?

A hollow cylinder, which is open at both ends, has a radius of $(3.0 \pm 0.1)cm$ and a length of $(15.0 \pm 0.1) cm$. What is the value, with its absolute uncertainty, of the surface area of the cylinder?

A ship of mass $8.4 \times 10^7 kg$ is approaching a harbour with speed 16.4ms⁻¹. By using reverse thrust it can maintain a constant total stopping force of 920 000 N. How long will it take to stop?

An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r and density ρ. The volume of a sphere is $(4/3)πr^3$. Which average pressure does the object exert on the table?

A probe is used to monitor the quality of the water in the sea. The probe is suspended by a vertical string which is attached to a sphere. The stationary sphere floats in equilibrium on the surface of the sea, as shown. The sphere has a weight of 5.00 N. The probe and string have a combined weight of 2.00 N. The density of the seawater is $1.03 \times 10^3kgm^{-3}$. The upthrust acting on the probe and thread is negligible. What is the volume of the sphere below the surface of the sea?

A beam of vertically polarised light is incident normally on a polarising filter. The filter can be rotated so that it is always in a plane perpendicular to the beam. The transmission axis of the filter is initially vertical. The filter is first rotated clockwise by an angle of 30° so that the transmitted light waves have intensity I₃₀. The filter is then rotated clockwise by a further angle of 30°. What is the new intensity of the transmitted light waves?