Philippine Physics Olympiad 2022
Qualifying Exam, Part A
9 April 2022
Problem 1
[1 point] Which of the following is closest to one nanocentury?
(a) 3 seconds
(b) 3 minutes
(c) 3 hours
(d) 3 days
(e) 3 weeks
Problem 2
[1 point] A projectile is launched with a purely horizontal initial velocity, from a height H above the ground.
The range of the projectile is H. Which of the following quantities is closest to the initial speed, v0 , of the
projectile?
p
(a) v0 = gH/3
p
(b) v0 = gH/2
√
(c) v0 = gH
√
(d) v0 = 2gH
√
(e) v0 = 3gH
Problem 3
[1 point] Three particles are located on the x-axis. The first particle has charge Q and is at x = −L. The
second particle has charge Q and is at x = 0. The third particle has charge KQ and is at x = L. The electric
field due to this three-particle system is zero at x = L/2. Which of the following numerical values is closest
to K?
(a) 1.0
(b) 1.1
(c) 1.3
(d) 1.5
(e) 1.7
Problem 4
[1 point] A uniform rope of length L = 10.0 meters and mass
M = 4.00 kg hangs vertically from a rigid support. A block
of mass m = 5.00 kg hangs from the free end of the rope.
A transverse pulse of wavelength 0.050 m is produced at the
lower end of the rope. The wavelength of the pulse when it
reaches the top of the rope is closest to:
(a) 0.050 m
(b) 0.056 m
(c) 0.062 m
(d) 0.075 m
(e) 0.112 m
Problem 5
[1 point] The P -V diagram in the figure illustrates the Sargent cycle for an ideal gas. Paths 1-2 and 3-4 are reversible
adiabatic, path 2-3 is at constant volume, and path 4-1 is at constant pressure. If Ti denotes the temperature at point i, which
temperature is hottest?
(a) indeterminate. (not enough information.)
(b) T1
(c) T2
(d) T3
(e) T4
Problem 6
[1 point] A 1.00 gram particle initially at rest is acted upon by a constant 1.00-newton force in a fixed
direction for 2.40 × 105 s. The speed of light in vacuum is approximately 2.998 × 108 m/s. The final speed
of the particle is closest to
(a) 0.5 c
(b) 0.6 c
(c) 0.7 c
(d) 0.8 c
(e) 0.9 c
Problem 7
[1 point] A geosynchronous orbit of a satellite (of mass m) around the Earth (of mass ME and radius RE ) is
one which has the same period as the Earth’s rotation. If the angular velocity of the Earth is ω, what is the
radius of the geosynchronous orbit?
p
GME /(RE ω 2 )
(a)
(b) 2Gm/(RE ω)2
(c) (GME /ω 2 )1/3
(d) GME /ω 2
(e) 2GME /ω 2
Problem 8
[1 point] The electric field inside a sphere of radius R is given by E = E0 zẑ. What is the total charge inside
the sphere?
(a) indeterminate. (not enough information.)
(b) (2π/3)0 E0 R3
(c) (4π/3)0 E0 R3
(d) 2π0 E0 R3
(e) 0
Problem 9
[1 point] Light from a laser enters a glass block at A and exits
at B. The glass block has length L and an index of refraction
n = 1.60. The angle of incidence is θ = 30.0◦ . With c the
speed of the light, the time needed for light to pass through the
block is closest to
(a) 1.60 L/c
(b) 1.70 L/c
(c) 1.80 L/c
(d) 1.90 L/c
(e) 2.00 L/c
Problem 10
[1 point] The figure shows a vertical cylindrical vessel separated
in two parts by a thin frictionless piston free to move along the
length of the vessel. The height of the cylinder is H = 100.0
cm and the piston divides the cylinder in the ratio 3:2. The
top part and the bottom part of the vessel respectively contain
n1 = 0.200 mole and n2 = 0.285 mole of an ideal gas. The
temperature of the gas is T = 300.0 K in each part. Use
g = 9.80 m/s2 and R = 8.314 J K−1 mol−1 . Which of the
following is closest to the mass of the piston?
(a) 3 kg
(b) 4 kg
(c) 5 kg
(d) 6 kg
(e) 7 kg
Problem 11
[1 point] A hydrogen atom spontaneously emits a photon associated with an electron transitioning from the
first excited state to the ground state. Which of the following is closest to the resulting magnitude of the
recoil velocity of the hydrogen atom?
Data:
Ionization energy of Hydrogen = 13.6 eV
Mass of Hydrogen atom: mH = 1.674 × 10−24 kg
Electron charge: −e = −1.602 × 10−19 C
Speed of light: c = 2.998 × 108 m/s
Planck’s constant: h = 6.626 × 10−34 J s
(a) 1.3 × 10−3 m/s
(b) 2.3 × 10−3 m/s
(c) 3.3 × 10−3 m/s
(d) 4.3 × 10−3 m/s
(e) 5.3 × 10−3 m/s
Problem 12
[1 point] A massless spring with spring constant k is vertically mounted so that bottom end is firmly
attached to the ground, and the top end free. A ball with mass m falls vertically down on the top end of the
spring, becoming attached, so that the ball oscillates vertically on the spring. What equation describes the
acceleration a of the ball when it is at a height y above the original position of the top end of the spring? Let
down be negative, and neglect air resistance; g is the magnitude of the acceleration of free fall.
(a) a = mv 2 /y + g
(b) a = mv 2 /y − g
(c) a = (k/m)y − g
(d) a = −(k/m)y + g
(e) a = −(k/m)y − g
Problem 13
[1 point] In a given inertial frame, two particles are shot out simultaneously from a given point, with equal
relativistic speeds v ∼ c, in orthogonal directions. What is the speed of each particle relative to the other?
(a) 2v
√
(b) 2v
p
√
(c) 2v/ 1 − v 2 /c2
p
(d) v 2 − 2v 2 /c2
p
(e) v 2 − v 2 /c2
Problem 14
[1 point] A polymer can be thought of as a giant molecule composed of many interlinked smaller molecules
called monomers. When polymers are immersed in water, they begin to shape into spheres with a distinct
size defined by the radius of gyration. Consider the data below showing the number of monomers and the
corresponding radius of gyration. The Flory relation is a scaling relation between the radius of gyration and
number of monomers, R = constant × N α .
Number of monomers
Radius of gyration (angstrom)
5
4.1
Based on the data, which of the following values is closest to α?
(a) 2/5
(b) 1/2
(c) 3/5
(d) 5/7
(e) 4/5
10
5.9
15
7.5
20
8.8
Problem 15
[1 point] Consider a semicircular object with radius R, mass
M , and uniform linear density. What is the moment of inertia
about an axis passing through the point X and perpendicular
to the plane of the wire?
(a) (1/2)M R2
(b) (3/4)M R2
(c) M R2
(d) (3/2)M R2
(e) 2M R2
Problem 16
[6 points] A projectile, on an inclined plane with angle of √
inclination θ, is launched horizontally with an initial velocity gL.
Let R(θ) and tf (θ)be the range and flight time, respectively, of
the projectile when the angle of inclination is θ. The flight time
is the time elapsed from the moment of launch to the moment
it hits the inclined plane. Which of the following is/are correct?
√
(a) R(45◦ ) = 2L
(b) R(30◦ ) = 2L/3
p
(c) tf (60◦ ) = 12L/g
p
(d) tf (45◦ ) = L/g
p
(e) tf (30◦ ) = 4L/(3g)
Problem 17
[6 points] A bimorph consists of two metal strips, A and B, with linear expansion coefficients αA = α
and αB = kα where 0 < k < 1. At 0◦ C each metal strip has length l0 , width w = l0 /10, and thickness
t = l0 /100.
When the temperature of the bimorph increases by ∆T , its cross-section assumes the shape of an annular
sector with thickness 2t, width w, and included angle θ. Neglect changes in the width and thickness of the
metal strips.
Which of the following are correct?
(a) When k = 3/4, θ = 50α∆T radian.
(b) When k = 4/5, θ = 30α∆T radian.
(c) When k = 9/10, θ = 10α∆T radian.
(d) When k = 19/20, θ = 4α∆T radian.
(e) When k = 99/100, θ = 2α∆T radian.
Problem 18
[6 points] At time t = 0, a ping-pong ball of radius R and mass M is released
√ from rest on an√incline with
◦
angle of inclination θ = 45 . The coefficients of kinetic friction are µk = 2/4 and µs = 3. Assume
that the moment of inertia about an axis passing through the center of the ping-pong ball is Icm = 2M R2 /3.
Which of the following statements about the dynamics of the ping-pong ball are correct?
Which of the following are correct?
(a) At time t > 0 the magnitude of the normal force acting on the ball is N = mg cos θ.
(b) At time t > 0 the magnitude of the friction force acting on the ball is f = µk mg cos θ.
(c) At time t > 0 the magnitude the of the ball’s translational acceleration is a = g(sin θ − µk cos θ).
(d) At time t > 0 the magnitude of the ball’s translational velocity is v = (3/5)gt sin θ.
(e) At time t > 0 the distance of the ball from its starting position is d = (1/2)g(sin θ − µk cos θ)t2 .
Problem 19
[6 points] A small block, with mass m, is on an incline with an angle of inclination of θ = 30◦ . One part, of
length L, of the incline is frictionless while the rest of the incline has nearly equal√coefficients of kinetic and
static friction µk ≈ µs ≈ µ = 1. The block is given an initial speed of v0 = k gL at time t = 0, where
k > 0. Denote the upward direction along the incline as the +s-direction, the position of the block at time
t = 0 as s = 0, and the maximum value of s reached by the block as smax .
Which of the following statements about smax are correct?
(a) When k = 1/3, smax = L/9.
(b) When k = 1/2, smax = L/4.
(c) When k = 2, smax = 4L.
(d) When k = 3, smax = (9 +
(e) When k = 4, smax
√
3)L/(1 +
√
= 16L/(1 + 3).
√
3).
Problem 20
[6 points] At time t = 0, Block A with mass mA = 2M is
moving to the right at a speed u and it is at a distance L from
a wall. Block A collides with Block B. Block B has mass
mB = M and is initially at rest and at a distance L/2 from
the wall. All collisions between Block A and Block B, and
between Block B and the wall are elastic. Neglect friction and
the linear dimensions of the blocks. Which of the following
statements are correct?
(a) Immediately after the first collision between Block A and Block B, the speed of Block A is u/3.
(b) Immediately after the first collision between Block A and Block B, the speed of Block B is 4u/3.
(c) Immediately after the second collision between Block A and Block B, the speed of Block A is 7u/9.
(d) Immediately after the second collision between Block A and Block B, the speed of Block B is u/9.
(e) There are exactly two collisions between Block A and Block B.
Problem 21
[6 points] Consider a region where there is a volume charge density ρ(r) = Krn whenever r < R, and
ρ(r) = 0 whenever r > R, where r is the distance from the origin, n is a number, and K is a positive
constant with the appropriate dimensions. Which of the following statements are correct?
(a) When n = 1, the total charge enclosed by the sphere of radius R/2 centered at the origin is πR4 K/12.
(b) When n = −1, the total charge enclosed by the sphere of radius R/2 centered at the origin is given
by Q = πR2 K/3.
(c) When n = −1, the magnitude of the electric field is uniform everywhere inside the sphere of radius
R centered at the origin.
(d) When n = 0, the magnitude of the electric field is uniform everywhere inside the sphere of radius R
centered at the origin.
(e) When n = 0, the magnitude of the electric field in the region r > R is KR3 /(30 r2 ).
Problem 22
[6 points] In the infinite resistor ladder shown in the figure, the battery has an emf of ε = 1 volt , R = 1Ω,
and α and β are positive numbers.
Which of the following statements about the circuit are correct?
(a) ε = I1 R + αI2 R.
(b) I1 = I2 + I3 .
√
17)] A.
√
(d) When α = 1/2 and β = 1/2, I2 = [2/(1 + 17)] A.
√
(e) When α = 1/2 and β = 1/2, I3 = [2/(1 + 17)] A.
(c) When α = 1/2 and β = 1/2, I1 = [4/(1 +
Problem 23
[6 points] At time t = 0, a particle with mass m and positive charge q is located at the origin of a coordinate
system (x, y, z)(t=0) = (0, 0, 0) and has initial velocity (vx , vy , vz )(t=0) = (u cos θ, u sin θ, 0) where u > 0,
and θ = 30◦ . The particle is in a region with uniform magnetic field B ẑ where B > 0. Which of the
following statements are correct?
(a) At time t = πm/(6qB), the x-coordinate of the particle is mu/qB.
(b) At time t = πm/(4qB), the x-coordinate of the particle is mu/qB.
(c) At time t = πm/(3qB), the x-coordinate of the particle is mu/qB.
(d) At time t = πm/(2qB), the x-coordinate of the particle is mu/qB.
(e) At time t = πm/(qB), the x-coordinate of the particle is mu/qB.
Problem 24
[6 points] Consider a double-slit interference experiment with d as the spacing between the two slits and L
as the distance to the viewing screen. Assume that L is very much larger than d. Which of the following
actions would cause the fringe spacing in the interference pattern to increase?
(a) Increasing the wavelength of light.
(b) Increasing the slit spacing.
(c) Increasing the distance to the viewing screen.
(d) Increasing the intensity of the light source.
(e) Submerging the entire experiment in water.
Problem 25
[6 points] A black body is at a temperature T0 at time t = 0, and is suspended in a room where the temperature
is close to absolute zero. Heat transfer through conduction and through convection are negligible. Let T (t)
be the temperature of the blackbody at time t. It is observed that the temperature of the black body is T0 /2
(in kelvins) when the time is t = τ . Which of the following statements are true?
(a) T (2τ ) < 0.40T0
(b) T (3τ ) > 0.35T0
(c) T (4τ ) < 0.30T0
(d) T (5τ ) > 0.25T0
(e) T (6τ ) < 0.20T0