“One of the deepsecrets of life is that all that is really worth the doing is what we do forothers.”

– Lewis Carroll

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

Today weshall discuss a few multiple choice practice questions relevant to AP Physics 1and AP Physics 2 courses. Questions (1), (2) and (3) are for AP Physics 1 whereas 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.

Similarlyquestions (4) and (5) are single correct answer type multiple choice questionswhere as question (6) is multi-correct answer type multiple choice question.

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

(a) 2*F*

(b) 4*F*

(c) 8*F*

(d) 16*F*

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

(a) *g*_{1}

(b) 2*g*_{1}

(c) 4*g*_{1}

**(3)** A loud speaker is excited with an alternating current of frequency 1000Hz. The sound produced by the loud speaker propagates in air along the x-axisthrough points P and Q (Fig.), which lie 5 m apart. Which of the followingstatements 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 agreater distance from the loud speaker.

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

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

**(4)** An electron is projected with uniform velocity **v** along the axisof a plane circular coil carrying a steady current. Which one among thefollowing statements is correct?

(a) The electron will continue to move along the axis with uniformacceleration

(b) The electron will move along a helical path around the axis of thecircular coil.

(c) The electron will continue to move along the axis with uniformacceleration or deceleration, depending on the direction of the current in thecoil

(d) The electron will continue to move along the axis with uniformvelocity **v**

**(5)** A beam of sun light is allowed to fall normally on one face of a glassslab of uniform thickness. Light of which component colour will emerge *last* through the opposite face of theslab?

(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 caron a straight road. In which of the following cases will the listener L note anapparent increase in the frequency of the sound emitted by the siren?

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

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

(c) S and L moving in the direction SL with speeds* u *and 2*u* 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 tothe mass of the sphere. The mass of sphere A is (4/3) π*R*^{3}d where as the mass of sphere B is (4/3) π(2*R*)^{3}(2*d*) = 16(4/3) π*R*^{3}d.

Since the mass of sphere B is 16 times the mass of Athe gravitational force on B is 16 times that on A. The answer is 16*F *[Option (d)].

**(2)** Acceleration = Force/Mass.

Even though the gravitational force on sphere B is16 times that on sphere A, the acceleration of sphere B is the same as that ofsphere A since the mass of sphere B is 16 times that of sphere A. The answer is*g*_{1 }[Option (a)].

**(3) **Sound is a longitudinal wave. In longitudinal wavesparticles of the medium vibrate parallel to the direction of propagation of thewave. 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 themedium through which the wave propagates. Therefore, option (b) is incorrect.

**(4)** The magnetic field due to a current carryingcircular 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 oranti-parallel to the direction of the magnetic field produced by the coil. Consequentlythe magnetic force on the electron is zero.

[The expression for the magnitude of the magneticforce *F* on a moving charge is *F = qvB *sin*θ* where *q* is the charge, *v *is the speed of the charge, *B *is the magnitude of the magnetic fluxdensity and *θ* is the angle betweenthe direction of motion of the charge and the direction of the magnetic field.In the present case *θ* is either zeroor 180º so that sin*θ* is zero].

Theelectron will therefore be unaffected and will continue to move with uniformvelocity **v** [Option (d)].

**(5)** Violet light hasthe least speed in a material medium. Therefore, light of violet colour willemerge last from the opposite face of the slab [Option (c)].

[Note that the refractive index of a material mediumfor violet light is maximum (since violet light is bent most). Since therefractive index of a medium is the ratio of the speed of light in free spaceto the speed in the medium, it follows that the speed is smaller if therefractive index is greater].

**(6)** Thisquestion involves Doppler effect, which is the phenomenon by which the frequency of awave 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 *v*_{S}, the listener move withvelocity *v*_{L} and the windblow with velocity *w*, all in the* same* direction as shown in the figure.

**Wind→ w S●→ v_{S} L●→v_{L}**

The apparent frequency (*n’*) of sound is then given by

*n’ = n*(*v + w *– *v*_{L})/ (*v +w *– *v*_{S}) ………………………(i)

where *n* isthe real frequency of the sound and *v*is the velocity of sound. It may be noted that the above relation has beenderived on the assumption that the source is moving towards the listener, thelistener is moving *away from *thesource and the wind is blowing *from thesource to the listener*.* *

Considering case (a), we have *n’ = n*(*v + *0 – *u*)/ (*v +*0* *– 2*u*)so that *n’ > n*

Considering case (b), we have *n’ = n*(*v + *0 + 2*u*)/ (*v +*0* *+ *u*) so that *n’> n*

[Note that the signs of *v*_{L} and *v*_{S}are negative in this case]

Considering case (c), we have *n’ = n*(*v + *0 – 2*u*)/ (*v +*0* *– *u*) so that *n’< n*

Considering case (d), we have *n’ = n*(*v + w* – 0)/ (*v +w *– 0) so that *n’ = n*

Thuscases (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 apparentfrequency increases if the source moves towards the listener (relatively) orthe listener moves towards the source (relatively). If they move away from eachother, the apparent frequency decreases].

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