POST UTME FUTA 2017 Physics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A block of mass $m$ is moving with a velocity $v$ on a frictionless surface. The block is subject to a cons\tant force $F$. What is the acceleration of the block?
A. \frac{F}{m}
B. \frac{mv}{F}
C. \frac{F}{mv}
D. \frac{mv^2}{F}
Question 2
A block of mass m is attached to a horizontal spring of spring cons\tant k. The block is displaced by a dis\tance x and then released. What is the angular frequency ω of the resulting simple harmonic motion?
A. \sqrt{\frac{k}{m}}
B. \sqrt{\frac{m}{k}}
C. \frac{k}{m}
D. \frac{m}{k}
Question 3
A particle of mass 2 kg is attached to a spring with a force cons\tant of 100 N/m. If the particle is displaced by 0.2 m from its equilibrium position and released from rest, what is its angular frequency?
A. 10 rad/s
B. 20 rad/s
C. 5 rad/s
D. 50 rad/s
Question 4
A photon of energy 2.5 eV is incident on a metal surface with work function 2.0 eV. What is the maximum kinetic energy of the emitted electron?
A. 0.5 eV
B. 1.0 eV
C. 1.5 eV
D. 2.0 eV
Question 5
A circuit consists of a 10 Ω resistor, a 20 Ω resistor, and a 5 Ω resistor connected in series. If a voltage of 12 V is applied across the circuit, what is the current through the 5 Ω resistor?
A. 0.4 A
B. 0.6 A
C. 0.8 A
D. 1.2 A
Question 6
A particle of mass $m$ is confined to a one-dimensional box of length $L$. The ground state wave function of the particle is given by \( psi_1\( x \ \) = \sqrt{\frac{2}{L}} \sinleft\( \frac{pi x}{L}\right \)). What is the probability of finding the particle in the region $0 < x < \frac{L}{2}$?
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{1}{8}
D. \frac{1}{16}
Question 7
A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$. If the particle's speed is $v$, what is its angular momentum $L$?
A. \frac{mv}{k}
B. \frac{mv^2}{k}
C. \frac{mv^2r}{k}
D. \frac{mv^3}{k}
Question 8
A beam of light passes from air into a glass of re\fractive index μ. If the angle of incidence is θ, derive an expression for the angle of re\fraction ϕ.
A. \sin(ϕ) = \sin(θ)/μ
B. \sin(ϕ) = μ\sin(θ)
C. \sin(ϕ) = \sin(θ)μ
D. \sin(ϕ) = μ\sin(θ)
Question 9
A uniform solid sphere of radius R and mass M is placed at the bottom of a frictionless inclined plane of angle θ. The sphere starts to roll up the plane without slipping. What is the minimum speed v0 at the bottom of the plane for the sphere to reach the top?
A. g \sinθ
B. g \sinθ / 2
C. g \sinθ / 3
D. g \sinθ / 4
Question 10
A block of mass $M$ is placed on a frictionless surface and connected to a horizontal spring with a spring cons\tant $k$. The block is displaced by a dis\tance $x$ from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, what is the angular frequency of the block's motion?
A. \sqrt{\frac{k}{M}}
B. \sqrt{\frac{M}{k}}
C. \frac{k}{M}
D. \frac{M}{k}
Question 11
A particle of mass m is attached to a spring of force cons\tant k. If the particle is displaced by a dis\tance x from its equilibrium position and released, derive an expression for the time period of oscillations.
A. T = 2π√\( m/k \)
B. T = 2π√\( k/m \)
C. T = 2π√(mk)
D. T = 2π√(km)
Question 12
A nucleus of mass number A and atomic number Z undergoes \beta decay. What is the resulting nucleus?
A. A' = A, Z' = Z + 1
B. A' = A, Z' = Z - 1
C. A' = A + 1, Z' = Z
D. A' = A - 1, Z' = Z
Question 13
A block of mass 5 kg is attached to a horizontal spring with a force cons\tant of 100 N/m. If the block is displaced by 2 m from its equilibrium position and released from rest, what is the maximum speed of the block?
A. 2 m/s
B. 4 m/s
C. 6 m/s
D. 8 m/s
Question 14
A beam of light passes from air into a glass of re\fractive index 1.5. If the angle of incidence is 30°, what is the angle of re\fraction?
A. 20°
B. 30°
C. 40°
D. 50°
Question 15
A photon of wavelength 500 nm is incident on a metal surface. If the work function of the metal is 2.5 eV, what is the maximum kinetic energy of the emitted electron?
A. 1.5 eV
B. 2.0 eV
C. 2.5 eV
D. 3.0 eV

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