## Pages

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

## Wednesday, May 30, 2012

### AP Physics B & C - Multiple Choice Practice Questions on One Dimensional Kinematics

"Whenever you are confronted with an opponent, conquer him with love."
– Mahatma Gandhi

Let us discuss a few interesting multiple choice practice questions on one dimensional motion. Here are some questions beneficial for AP Physics B as well as AP Physics C aspirants:
(1) The adjoining figure shows the velocity time graph of an object. Total displacement suffered by the object during the interval when it has non-zero acceleration and retardation is
(a) 80 m
(b) 70 m
(c) 60 m
(d) 40 m
(e) 30 m
The object has non-zero acceleration and retardation during the time intervals from 5 sec to 15 sec and from 20 sec to 30 sec. The total area under the velocity time graph during these intervals gives the required displacement.
Displacement from 5 sec to 15 sec = 30 m
Displacement from 20 sec to 30 sec = 40 m
Therefore, total displacement = 70 m
(2) Successive positions (x) of an object (moving from left to right) at equal time intervals are shown in the following figure:

Which one among the following position-time graphs best represents the motion of the object? Change of position is slowest in the beginning and in the end. The motion is best represented by graph (c).
[Note that graph (d) is not the answer since the change of position in the beginning and in the end is shown as fastest in it]
(3) Which one among the following velocity-time graphs best represents the motion of the object mentioned in question no.(2)?

The graph (c) is the answer.
The following questions are meant for AP Physics C aspirants:
(4) A particle projected vertically upwards attains the maximum height h in time t. While returning from the highest point it takes an additional time t1 to fall to the height h.2. If air resistance is negligible, how is t1 related to t?
(a) t1 = t/2
(b) t1 = √(t/2)
(c) t1 = t/2
(d) t1 = t/3
(e) t1 = t/3
For the upward motion we have
0 – u2 = – 2gh …………(i)
[We have used the equation of motion, v2 u2 = 2as. The sign of the gravitational acceleration g is negative since it is opposite to the direction of the velocity of projection u]
Using the equation of motion, v = u + at we have
0 = u gt from which u = gt
Substituting this value of u in Eq (i), we have
g2t2 = 2gh
Therefore, t =√(2h/g) ……..(ii)
For the fall through h/2 from the highest point we have
h/2 = 0×t1 + ½ gt12
[We have used the equation of motion, s = ut + ½ gt2]
Therefore, t1 =√(h/g)
Comparing this with the value of t given in Eq (ii) we obtain t1 = t/2.
(5) A ball projected vertically up has the same vertical displacement h at times t1 second and t2 second. If air resistance is negligible, the maximum height reached by the ball is
(a) gt1t2/2
(b) g(t12 + t22)/2
(c) g(t1 + t2)2/4
(d) g(t1 + t2)2/8
(e) 2g(t1 + t2)2
The time taken by the ball to move from height h to the top of its trajectory and back to the height h is t2 t1. Therefore, the time taken to move from height h to the top of the trajectory is (t2 t1)/2.
The total time taken for the upward journey (from ground to the top most point) is evidently t1 + t2 t1)/2 = (t1 + t2)/2.
Time taken for the return journey (from the top most point to the ground) also is equal to (t1 + t2)/2. Therefore, the maximum height H (using the equation, s = ut + ½ gt2) is given by
H = 0 + ½ g [(t1 + t2)/2]2
Or, H = g(t1 + t2)2/8
Questions on kinematics were discussed earlier on this site. You can access them either by clicking on the label ‘kinematics’ below this post or by trying a search for                  ‘kinematics’ using the search box provided on this page.

## Monday, May 7, 2012

### AP Physics B - Multiple Choice Practice Questions on Atomic Physics and Quantum Effects

"Men often become what they believe themselves to be. If I believe I cannot do something, it makes me incapable of doing it. But when I believe I can, then I acquire the ability to do it even if I didn't have it in the beginning
– Mahatma Gandhi

AP Physics 2012 exams are just a few days away. Your final preparations for the exam must be in full swing and there is no time to waste. Today I give you a few multiple choice practice questions on atomic physics and quantum effects. Questions in this section posted earlier on this site (with solution) can be accessed by clicking on the label ‘atomic physics and quantum effects’ given below this post. Or, you may try a search for ‘atomic physics and quantum effects’ using the search box provided on this page.

(1) The adjoining figure shows the graphical relation between the frequency of incident radiation and the magnitude of stopping potential in the case of metals A and B. Note that the straight line graphs have the same slope. Which one among the following statements is correct in this case?
(a) A and B have the same work function
(b) A and B have the same threshold wave length
(c) Maximum kinetic energy of photoelectron in the case of metals A and B is directly proportional to the increment in frequency of incident radiation over the threshold frequency.
(d) Metal B is a better photosensitive material than metal A.
(e) For a given change in the frequency of incident radiation, the changes in stopping potentials are different for metals A and B
Since we have straight line graphs for both metals, maximum kinetic energy of photoelectron is directly proportional to the increment in frequency of incident radiation over the threshold frequency. Therefore option (c) is correct.
(2) The de Broglie wave length of a particle can be reduced to half its initial value by changing its kinetic energy to
(a) half the initial value
(b) twice the initial value
(c) three times the initial value
(d) four times the initial value
(e) a quarter of the initial value
Kinetic energy E of a body of mass m is given by
E = p2/2m where p is the momentum
[This follows from E = ½ mv2 = m2v2/2m. Here v is the velocity and mv = p]
The above relation shows that the kinetic energy becomes four times when the momentum is doubled.
The de Broglie wave length λ is given by
λ = h/p where h is Planck’s constant.
Therefore, the de Broglie wave length of a particle can be reduced to half its initial value by changing its momentum to twice the initial value. Evidently the kinetic energy of the particle the becomes four times the initial value [Option (d)].
[Suppose the above question is modifie as follows:
A particle has de Broglie wave length λ when its kinetic energy is E. What additional kinetic energy is to be aded to it in order to reduce the de Broglie wave length to λ/2?
(a) E
(b) 2E
(c) 3E
(d) 4E
(e) E/4
The answer is 3E since you are asked to find the additional kinetic energy].
(3) Uranium (atomic number 92) has an isotope of mass number 235. It can undergo successive disintegrations to get transformed into lead (82Pb207). How many α-particles and β-particles are emitted during this transformation?
(a) α = 7, β = 4
(b) α = 4, β = 3
(c) α = 7, β = 0
(d) α = 7, β = 7
(e) α = 4, β = 7
Beta particle emission does not affect the mass number. In order to reduce the mass number by 28 (from 235 to 207), the number of α-particles to be emitte must be 7. Since each α-particles carries two fundamental units of positive charge, the atomic number of the end product gets reduced by 14. But the final product (82Pb207) has its atomic number reduced by 10 only. The extra 4 units must be obtained by the emission of four β-particles. The correct option therefore ia (a).
[Note that when a β-particles (electron) is emitted from the nucleus, the nuclear charge increases by one unit. This happens as a result of the transformation of a neutron in the nucleus into a proton].
(4) Fundamental forces in nature are gravitational force, electromagnetic force, nuclear force and weak force. If these forces act over very short distances of the order of nuclear dimensions, how do you arrange them in decreasing order (starting with the strongest?
(a) Gravitational force, electromagnetic force, nuclear force, weak force
(b) Electromagnetic force, gravitational force, nuclear force, weak force
(c) Electromagnetic force, nuclear force, weak force, gravitational force
(d) Gravitational force, nuclear force, electromagnetic force, weak force
(e) Nuclear force, electromagnetic force, weak force, gravitational force
The correct option is (d).
[Don’t get carried away by the term ‘weak force’. The weakest force is gravitational force where as the strongest is nuclear force].
(5) Two protons are separated by a distance of 50 Ǻ. If the electromagnetic force between them is F1 and the nuclear force between them is F2, which one among the following is the most reliable statement?
(a) F1 >> F2
(b) F2 >> F1
(c) F1 > F2
(d) F2 > F1
(e) F2 = F1
This question is similar to question No. (4) in the sense that it is meant for checking your knowledge of nuclear physics. The correct option is (a). Nuclear  force is a very short range force. At a separation of 50 Ǻ which is very large compared to the size of a nucleus, nuclear force (strong interaction) between two protons is negligible compared to the electrostatic force. Therefore the correct option is (a).