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POST UTME FUTA 2017 Physics | Objective

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Question 1 View Details

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?

Correct A. 10 rad/s

B. 20 rad/s

C. 5 rad/s

D. 50 rad/s

Correct Answer: A

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Question 2 View Details

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

Correct C. 0.8 A

D. 1.2 A

Correct Answer: C

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Question 3 View Details

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If air resis\tance is neglected, what is the maximum height reached by the projectile?

A. 10 m

Correct B. 20 m

C. 30 m

D. 40 m

Correct Answer: B

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Question 4 View Details

A magnetic field of 0.5 T is applied to a coil of 100 turns and a radius of 0.1 m. If the coil is rotated at a frequency of 50 Hz, what is the induced emf?

A. 0.1 V

B. 0.5 V

Correct C. 1 V

D. 5 V

Correct Answer: C

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Question 5 View Details

A current of 2 A flows through a resistor of 10 Ω. If the voltage across the resistor is 20 V, what is the power dissipated?

Correct A. 40 W

B. 20 W

C. 10 W

D. 5 W

Correct Answer: A

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Question 6 View Details

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 $0 < x < \frac{L}{2}$?

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{1}{8}

D. \frac{1}{16}

Correct Answer: A

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Question 7 View Details

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?

Correct A. \sqrt{\frac{k}{M}}

B. \sqrt{\frac{M}{k}}

C. \frac{k}{M}

D. \frac{M}{k}

Correct Answer: A

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Question 8 View Details

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by a voltage source $V_0$ with a frequency $f$. Assuming the circuit is in resonance, what is the impedance of the circuit?

A. R

B. \sqrt{L^2 + C^2}

Correct C. \frac{1}{\sqrt{LC}}

D. \frac{R}{\sqrt{LC}}

Correct Answer: C

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Question 9 View Details

A radioactive sample decays with a half-life of $T_{1/2}$. What is the activity of the sample after a time $t$?

Correct A. A_0 e^{-\lambda t}

B. A_0 e^{\lambda t}

C. A_0 + \lambda t

D. A_0 - \lambda t

Correct Answer: A

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Question 10 View Details

A parallel plate capacitor has a capaci\tance of $C$. The plates are separated by a dis\tance $d$ and have a surface charge density of $\sigma$. What is the electric field between the plates?

Correct A. \frac{\sigma}{\epsilon_0}

B. \frac{2\sigma}{\epsilon_0}

C. \frac{\sigma}{2\epsilon_0}

D. \frac{2\sigma}{d}

Correct Answer: A

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Question 11 View Details

A solid sphere of radius R and mass M is floating in a liquid of density ρ. If the sphere is displaced slightly from its equilibrium position, it will experience an upward buoyant force equal to the weight of the liquid displaced. U\sing the principle of conservation of energy, derive an expression for the time period of small oscillations of the sphere.

Correct A. T = 2π√$ 3ρV/Mg $

B. T = 2π√$ ρV/Mg $

C. T = 2π√$ 3ρV/M $

D. T = 2π√$ ρV/M $

Correct Answer: A

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Question 12 View Details

A parallel plate capacitor consists of two plates of area A and separation d, with a dielectric of permittivity ε between them. If a potential difference V is applied across the plates, derive an expression for the capaci\tance C.

Correct A. C = εA/d

B. C = εA/2d

C. C = εA/3d

D. C = εA/4d

Correct Answer: A

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Question 13 View Details

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.

Correct A. \sin(ϕ) = \sin(θ)/μ

B. \sin(ϕ) = μ\sin(θ)

C. \sin(ϕ) = \sin(θ)μ

D. \sin(ϕ) = μ\sin(θ)

Correct Answer: A

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Question 14 View Details

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.

Correct A. T = 2π√$ m/k $

B. T = 2π√$ k/m $

C. T = 2π√(mk)

D. T = 2π√(km)

Correct Answer: A

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Question 15 View Details

A photon of energy E is incident on a metal surface of work function W. If the photon is not absorbed, derive an expression for the maximum kinetic energy of the ejected electron.

Correct A. K_max = E - W

B. K_max = E + W

C. K_max = W - E

D. K_max = W + E

Correct Answer: A

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Question 16 View Details

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?

Correct A. g \sinθ

B. g \sinθ / 2

C. g \sinθ / 3

D. g \sinθ / 4

Correct Answer: A

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Question 17 View Details

A particle of mass m is moving in a circular orbit of radius r under the influence of a central force given by F = k / r^2. What is the angular momentum L of the particle?

Correct A. mv^2 r / k

B. mv^2 r^2 / k

C. mv^2 r / k^2

D. mv^2 r^2 / k^2

Correct Answer: A

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Question 18 View Details

A beam of light passes from air into a glass of re\fractive index μ. What is the angle of re\fraction θ2?

Correct A. \sin^{-1} $ \frac{\mu}{1} $

B. \sin^{-1} $ \frac{1}{\mu} $

C. \tan^{-1} $ \frac{\mu}{1} $

D. \tan^{-1} $ \frac{1}{\mu} $

Correct Answer: A

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Question 19 View Details

A nucleus of mass number A and atomic number Z undergoes \beta decay. What is the resulting nucleus?

Correct A. A' = A, Z' = Z + 1

B. A' = A, Z' = Z - 1

C. A' = A + 1, Z' = Z

D. A' = A - 1, Z' = Z

Correct Answer: A

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Question 20 View Details

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?

Correct A. \sqrt{\frac{k}{m}}

B. \sqrt{\frac{m}{k}}

C. \frac{k}{m}

D. \frac{m}{k}

Correct Answer: A

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Question 21 View Details

A parallel plate capacitor has a capaci\tance of 10 μF and is charged to a potential difference of 12 V. If the dis\tance between the plates is doubled, what is the new potential difference?

A. 6 V

B. 12 V

Correct C. 24 V

D. 48 V

Correct Answer: C

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Question 22 View Details

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°

Correct B. 30°

C. 40°

D. 50°

Correct Answer: B

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Question 23 View Details

A nucleus of mass number 240 and atomic number 94 undergoes \alpha decay. What is the mass number of the daughter nucleus?

Correct A. 236

B. 238

C. 240

D. 242

Correct Answer: A

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Question 24 View Details

A block of mass 5 kg is attached to a spring of spring cons\tant 200 N/m. If the block is displaced by 0.2 m from its equilibrium position and released, what is the maximum speed of the block?

A. 2 m/s

Correct B. 4 m/s

C. 6 m/s

D. 8 m/s

Correct Answer: B

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Question 25 View Details

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

Correct C. 1.5 eV

D. 2.0 eV

Correct Answer: C

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