Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

A

An ion moves in a circle in a uniform magnetic field. Which single change would increase the radius of the circular path?

A. Decreasing the speed of the ion

B. Increasing the charge of the ion

C. Increasing the mass of the ion

D. Increasing the strength of the magnetic field

C

An object at the end of a wooden rod rotates in a vertical circle at a constant angular velocity. What is correct about the tension in the rod? 

A. It is greatest when the object is at the bottom of the circle.
B. It is greatest when the object is halfway up the circle. 
C. It is greatest when the object is at the top of the circle. 
D. It is unchanged throughout the motion.

A

A particle of mass m and charge of magnitude q enters a region of uniform magnetic field B that is directed into the page. The particle follows a circular path of radius R. What are the sign of the charge of the particle and the speed of the particle?

B

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A. $\frac{T}{4}$

B. $\frac{T}{2}$

C. $\frac{3T}{4}$

D. T

B

The mass at the end of a pendulum is made to move in a horizontal circle of radius r at constant speed. The magnitude of the net force on the mass is F.

What is the direction of F and the work done by F during half a revolution?

A

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

A

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

C

On Mars, the gravitational field strength is about $\frac{1}{4}$ of that on Earth. The mass of Earth is approximately ten times that of Mars.

What is $\frac{\text{radius of Earth}}{\text{radius of Mars}}$ ?

A. 0.4

B. 0.6 

C. 1.6 

D. 2.5

C

Two satellites of mass m and 2m orbit a planet at the same orbit radius. If F is the force exerted on the satellite of mass m by the planet and a is the centripetal acceleration of this satellite, what is the force and acceleration of the satellite with mass 2m?

A

The gravitational field strength at the surface of Earth is g. Another planet has double the radius of Earth and the same density as Earth. What is the gravitational field strength at the surface of this planet?

A.  $\frac{g}{2}$

B.  $\frac{g}{4}$

C.  2g

D.  4g

C

An object of constant mass is tied to the end of a rope of length l and made to move in a horizontal circle. The speed of the object is increased until the rope breaks at speed v. The length of the rope is then changed. At what other combination of rope length and speed will the rope break?

A

A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc.

Point X is a distance 2L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a.

What is the linear speed and centripetal acceleration of point X?

B

Mass $M$ is attached to one end of a string. The string is passed through a hollow tube and mass $m$ is attached to the other end. Friction between the tube and string is negligible.

Mass $m$ travels at constant speed $v$ in a horizontal circle of radius $r$. What is mass $M$?

A.  $\frac{m{v}^2}{r}$

B.  $m{v}^{2}rg$

C.  $\frac{mg{v}^2}{r}$

D.  $\frac{m{v}^2}{gr}$

D

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

C

A child stands on a horizontal rotating platform that is moving at constant angular speed. The centripetal force on the child is provided by 

A. the gravitational force on the child.

B. the friction on the child’s feet.

C. the tension in the child’s muscles.

D. the normal reaction of the platform on the child.

B

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

B

A sphere is suspended from the end of a string and rotates in a horizontal circle. Which freebody diagram, to the correct scale, shows the forces acting on the sphere? 

D

A satellite is orbiting Earth in a circular path at constant speed. Three statements about the resultant force on the satellite are:

I.   It is equal to the gravitational force of attraction on the satellite.
II.  It is equal to the mass of the satellite multiplied by its acceleration.
III. It is equal to the centripetal force on the satellite.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

D

This was a good discriminator at HL although many candidates chose option B (D correct). Option B was just the most popular choice at SL. Candidates appear not to realise that although this is circular motion F = ma still applies.

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

D

A mass at the end of a string is swung in a horizontal circle at increasing speed until the string breaks.

The subsequent path taken by the mass is a

A.     line along a radius of the circle.

B.     horizontal circle.

C.     curve in a horizontal plane.

D.     curve in a vertical plane.

D

A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

A. $\frac{T}{2}$

B. T

C. $\sqrt{2T}$

D. 2T

B

A ball of mass 0.3 kg is attached to a light, inextensible string. It is rotated in a vertical circle. The length of the string is 0.6 m and the speed of rotation of the ball is 4 m s⁻¹.

What is the tension when the string is horizontal?

A.  5 N

B.  8 N

C.  11 N

D.  13 N

B

This question was well answered by both HL and SL candidates with a high difficulty index for each paper.

An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.

What is the tension in the string when the object is at the bottom of the circle?

A.     m(ω²r + g)

B.     m(ω²r – g)

C.     mg(ω²r + 1)

D.     mg(ω²r – 1)

A

A mass attached to a string rotates in a gravitational field with a constant period in a vertical plane.

How do the tension in the string and the kinetic energy of the mass compare at P and Q?

B

A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3$\pi$ rad s^-1. 

What is the magnitude and direction of the force responsible for this motion?

D

A mass at the end of a string is moving in a horizontal circle at constant speed. The string makes an angle θ to the vertical.

What is the magnitude of the acceleration of the mass?

A.  g

B.  g sin θ

C.  g cos θ

D.  g tan θ

D

Three statements about Newton’s law of gravitation are:

I.   It can be used to predict the motion of a satellite.
II.  It explains why gravity exists.
III. It is used to derive the expression for gravitational potential energy.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

B

Comments suggested that 'gravitational potential' is more suitable for an HL question. However, candidates should have realised that statement II is incorrect so option B is the only possibility and this proved the most popular answer. The wording will be altered to 'gravitational potential energy' for publication.

Which graph shows the relationship between gravitational force F between two point masses and their separation r?

D

Newton’s law of gravitation

A.     is equivalent to Newton’s second law of motion.

B.     explains the origin of gravitation.

C.     is used to make predictions.

D.     is not valid in a vacuum.

C

An object moves in a circle of constant radius. Values of the centripetal force $F$ are measured for different values of angular velocity $\omega$. A graph is plotted with $\omega$ on the $x$-axis. Which quantity plotted on the $y$-axis will produce a straight-line graph?

A.  $\sqrt{F}$

B.  $F$

C.  $F^2$

D.  $\frac{1}{F}$

A

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

C

A motorcyclist is cornering on a curved race track.

Which combination of changes of banking angle θ and coefficient of friction μ between the tyres and road allows the motorcyclist to travel around the corner at greater speed?

A

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

B

A satellite travels around the Earth in a circular orbit. What is true about the forces acting in this situation?

A. The resultant force is the same direction as the satellite’s acceleration.

B. The gravitational force acting on the satellite is negligible.

C. There is no resultant force on the satellite relative to the Earth.

D. The satellite does not exert any force on the Earth.

A