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`“Life is like riding a bicycle.  To keep your balance you must keep moving.”–Albert Einstein`

Friday, April 24, 2015

AP Physics 2 - Multiple Choice Practice Questions Involving Magnetic Fields

“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.”
– Richard Feynman

Questions involving magnetic fields are generally simple and interesting. But questions which appear simple at the first glance may tempt you to commit mistakes.

Here are a few multiple choice practice questions (single correct answer type) in this section:

(1) An electron is projected at right angles to a uniform magnetic field. The quantity that remains constant is

(a) velocity of electron

(b) momentum of electron

(c) kinetic energy of electron

(d) all the above

The velocity and momentum of the electron get changed since the direction of motion of the electron within the magnetic field changes continuously. However, the kinetic energy of the electron remains constant since the magnitudes of the velocity and momentum remain constant. Therefore, the correct option is (c).

(2) An electron is projected at right angles to a magnetic field that changes in magnitude with time. The quantity that remains constant is

(a) kinetic energy of electron

(b) momentum of electron

(c) velocity of electron

(d) none of the above

Since the magnetic field is changing, an emf is induced. The speed of the electron is changed and therefore the velocity, momentum and the kinetic energy are changed. The correct option is (d).

[Note that the particle accelerator betatron works on the principle of the production of an accelerating emf due to a changing magnetic field]
(3) Two very long straight conductors are arranged perpendicular to the XY plane. Their mid points are at A and B and are at the same distance ‘a’ from the origin (Fig.). Each conductor carries a current ‘I’ in the negative z-direction. What is the direction of the resultant magnetic field at the origin?

(a) along OP

(b) along OQ

(c) along OR

(d) along OS

The magnetic field produced at the origin O by the current in the conductor located at A is directed along OY.

[Note that the current is directed normally into the plane of the figure. You may use Maxwell’s cork screw rule or the right hand palm rule to obtain the direction of the magnetic field].

The magnetic field produced at the origin O by the current in the conductor located at B is directed along OX’. Since the magnetic fields produced at O by the two conductors are of the same magnitude, the resultant magnetic field at O is equally inclined to OY and OX’ and is directed along OP.

4) In question No. (3) the magnitude of the resultant magnetic flux density at the origin O is

(a) Î¼0 I/2Ï€a

(b) (√2) Î¼0 I/2Ï€a

(c) Î¼0 I/Ï€a

(d) 2 Î¼0 I/Ï€a

The magnetic flux density at distance a from a long conductor carrying current I is Î¼0 I/2Ï€a. Therefore, the resultant magnetic flux density at the origin O due to the two flux densities directed along OY and OX’ which are at right angles is √[( Î¼0 I/2Ï€a)2 + ( Î¼0 I/2Ï€a)2]= (√2) Î¼0 I/2Ï€a, as given in option (b).

(5) A bar magnet placed in a non-uniform magnetic field will experience

(a) a torque, but no net force

(b) a net force, but no torque

(c) neither a net force nor a torque

(d) a net force as well as a torque

If a bar magnet is located in a uniform magnetic field, the poles of the magnet will experience forces of equal magnitude, but of opposite direction. The net force acting on the magnet will therefore be zero. But the two equal and opposite forces will produce a torque which will try to rotate the bar magnet. If the magnetic field is non-uniform, the forces acting on the poles of the magnet will be of unequal magnitude so that in addition to a torque, there will be a net force on the magnet [Option (d)].

Saturday, August 16, 2014

AP Physics 1 and 2 – Multiple Choice Practice Questions

“One of the deep secrets of life is that all that is really worth the doing is what we do for others.”
– Lewis Carroll

As you know, with effect from the academic year 2014 – 2015, AP Physics B course is discontinued and is replaced by two new courses, namely AP Physics 1 and AP Physics 2. Both courses are algebra based. It is hoped that the new courses will help the students to explore deeper into key concepts in physics both in theory and practice.

Today we shall discuss a few multiple choice practice questions relevant to AP Physics 1 and AP Physics 2 courses. Questions (1), (2) and (3) are for AP Physics 1 where as questions (4) , (5) and (6) are for AP Physics 2.

Questions (1) and (2) are single correct answer type multiple choice questions where as question (3) is multi-correct answer type multiple choice question.

Similarly questions (4) and (5) are single correct answer type multiple choice questions where as question (6) is multi-correct answer type multiple choice question.

(1) The magnitude of the gravitational force on a solid sphere A of radius R and density d at a point P in the earth’s atmosphere is F. If this sphere is replaced by another solid sphere B of radius 2R and density 2d, the magnitude of the gravitational force acting on it will be

(a) 2F

(b) 4F

(c) 8F

(d) 16F

(2) The sphere A in question number (1) starts to fall freely under earth’s gravity with an acceleration of magnitude g1. What will be the magnitude of the acceleration of free fall of sphere B under earth’s gravity?

(a) g1

(b) 2g1

(c) 4g1

(d) 16g1

(3) A loud speaker is excited with an alternating current of frequency 1000 Hz. The sound produced by the loud speaker propagates in air along the x-axis through points P and Q (Fig.), which lie 5 m apart. Which of the following statements are true in this context?

(a) Air molecules at P and Q vibrate parallel to the x-axis

(b) The speed of sound at Q is less than the speed at P since Q is at a greater distance from the loud speaker.

(c) Air molecules at P are carried along the x-axis to the point Q and then farther away from Q.

(d) Air molecules at P and Q always maintain their mean positions at P and Q.

(4) An electron is projected with uniform velocity v along the axis of a plane circular coil carrying a steady current. Which one among the following statements is correct?
(a) The electron will continue to move along the axis with uniform acceleration
(b) The electron will move along a helical path around the axis of the circular coil.
(c) The electron will continue to move along the axis with uniform acceleration or deceleration, depending on the direction of the current in the coil
(d) The electron will continue to move along the axis with uniform velocity v

(5) A beam of sun light is allowed to fall normally on one face of a glass slab of uniform thickness. Light of which component colour will emerge last through the opposite face of the slab?
(a) Green
(b) Red
(c) Violet
(d) All colours will emerge simultaneously

(6) S is a police vehicle which sounds a siren and L is a listener in a car on a straight road. In which of the following cases will the listener L note an apparent increase in the frequency of the sound emitted by the siren?

(a) S and L moving in the direction SL with speeds 2u and u respectively.

(b) S and L moving in the direction LS with speeds u and 2u respectively.

(c) S and L moving in the direction SL with speeds u and 2u respectively

(d) S and L stationary and wind blowing in the direction SL with speed u.

Now, let us answer the above questions:
(1) The gravitational force is directly proportional to the mass of the sphere. The mass of sphere A is (4/3) Ï€R3d where as the mass of sphere B is (4/3) Ï€(2R)3(2d) = 16(4/3) Ï€R3d.
Since the mass of sphere B is 16 times the mass of A the gravitational force on B is 16 times that on A. The answer is 16F [Option (d)].

(2) Acceleration = Force/Mass.
Even though the gravitational force on sphere B is 16 times that on sphere A, the acceleration of sphere B is the same as that of sphere A since the mass of sphere B is 16 times that of sphere A. The answer is g1 [Option (a)].

(3) Sound is a longitudinal wave. In longitudinal waves particles of the medium vibrate parallel to the direction of propagation of the wave. Option (a) is correct. When a wave propagates through a medium, particles of the medium just vibrate about their position and are not carried along with the wave. Therefore, option (d) is correct and (c) is incorrect. The speed of a wave depends only on the properties of the medium through which the wave propagates. Therefore, option (b) is incorrect.

(4) The magnetic field due to a current carrying circular coil at any point on its axis is directed along the axis. Therefore, the electron projected along the axis of the coil moves either parallel or anti-parallel to the direction of the magnetic field produced by the coil. Consequently the magnetic force on the electron is zero.
[The expression for the magnitude of the magnetic force F on a moving charge is F = qvB sinÎ¸ where q is the charge, v is the speed of the charge, B is the magnitude of the magnetic flux density and Î¸ is the angle between the direction of motion of the charge and the direction of the magnetic field. In the present case Î¸ is either zero or 180Âº so that sinÎ¸ is zero].
The electron will therefore be unaffected and will continue to move with uniform velocity v [Option (d)].

(5) Violet light has the least speed in a material medium. Therefore, light of violet colour will emerge last from the opposite face of the slab [Option (c)].
[Note that the refractive index of a material medium for violet light is maximum (since violet light is bent most). Since the refractive index of a medium is the ratio of the speed of light in free space to the speed in the medium, it follows that the speed is smaller if the refractive index is greater].

(6) This question involves Doppler effect, which is the phenomenon by which the frequency of a wave as measured by an observer is changed because of the motion of the source, observer and the medium.
Let the source S of sound (fig.) move with velocity vS, the listener move with velocity vL and the wind blow with velocity w, all in the same direction as shown in the figure.

Wind→ w         S●→vS        L●→vL

The apparent frequency (n’) of sound is then given by
n’ = n(v + w vL)/ (v + w vS) ………………………(i)
where n is the real frequency of the sound and v is the velocity of sound. It may be noted that the above relation has been derived on the assumption that the source is moving towards the listener, the listener is moving away from the source and the wind is blowing from the source to the listener.
Considering case (a), we have n’ = n(v + 0 u)/ (v + 0 2u) so that n’ > n
Considering case (b), we have n’ = n(v + 0 + 2u)/ (v + 0 + u) so that n’ > n
[Note that the signs of vL and vS are negative in this case]
Considering case (c), we have n’ = n(v + 0 – 2u)/ (v + 0 u) so that n’ < n
Considering case (d), we have n’ = n(v + w – 0)/ (v + w – 0) so that n’ = n
Thus cases (a) and (b) are the correct options.
[Even if you don’t remember the above expression (i), you will be able to answer many questions if you note that the apparent frequency increases if the source moves towards the listener (relatively) or the listener moves towards the source (relatively). If they move away from each other, the apparent frequency decreases].

You can access all posts on waves on this site by clicking on the label ‘wave motion (including sound)’