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POST UTME FUTO 2018 Physics | Objective

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Question 1 View Details

A parallel plate capacitor has plates of area 0.04 m^2 and separation 3 mm. If the dielectric cons\tant of the material between the plates is 3.2, calculate the capaci\tance.

A. 1.6 x 10^-9 F

B. 3.2 x 10^-9 F

Correct C. 6.4 x 10^-9 F

D. 12.8 x 10^-9 F

Correct Answer: C

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Question 2 View Details

A gas at 300 K and 1 atm expands to twice its original volume. What is the final temperature?

A. 200 K

Correct B. 400 K

C. 600 K

D. 800 K

Correct Answer: B

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Question 3 View Details

A block of mass 2 kg is attached to a spring with spring cons\tant 100 N/m. If the block is displaced by 0.1 m and released, what is the maximum speed?

A. 0.5 m/s

B. 1 m/s

Correct C. 1.5 m/s

D. 2 m/s

Correct Answer: C

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Question 4 View Details

A circuit consists of a 12 V battery, a 4 Ω resistor, and a 2 Ω resistor connected in parallel. What is the total resis\tance?

A. 1.5 Ω

Correct B. 2 Ω

C. 2.5 Ω

D. 3 Ω

Correct Answer: B

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Question 5 View Details

A magnetic field of 0.5 T is applied to a coil of 100 turns and radius 0.1 m. What is the induced emf?

A. 0.1 V

Correct B. 0.5 V

C. 1 V

D. 2 V

Correct Answer: B

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Question 6 View Details

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The wave function of the particle is given by $psi(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{npi x}{L}\right $$, where $n$ is a positive integer. What is the expectation value of the position of the particle?

Correct A. L/2

B. nL/π

C. L/π

D. 2L/π

Correct Answer: A

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Question 7 View Details

A block of mass $M$ is placed on a horizontal surface. A horizontal force $F$ is applied to the block, cau\sing it to accelerate at a rate $a$. What is the coefficient of kinetic friction between the block and the surface?

Correct A. F/Mg

B. F/$ Mg + Fa $

C. Fa/$ Mg + Fa $

D. Fa/Mg

Correct Answer: A

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Question 8 View Details

A radioactive sample decays according to the equation $N(t) = N_0 e^{-\lambda t}$, where $N(t)$ is the number of nuclei remaining at time $t$, $N_0$ is the initial number of nuclei, and $\lambda$ is the decay cons\tant. What is the half-life of the sample?

Correct A. \frac{\ln 2}{\lambda}

B. \frac{\ln 2}{\lambda^2}

C. \frac{\lambda}{\ln 2}

D. \frac{\lambda^2}{\ln 2}

Correct Answer: A

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Question 9 View Details

A magnetic field is produced by a current-carrying wire. The magnetic field at a dis\tance $r$ from the wire is given by $B(r) = \frac{\mu_0 I}{2\pi r}$. What is the direction of the magnetic field at a dis\tance $r$ from the wire?

Correct A. \hat{\phi}

B. -\hat{\phi}

C. \hat{r}

D. -\hat{r}

Correct Answer: A

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Question 10 View Details

A sound wave is produced by a vibrating string. The frequency of the sound wave is given by $f = \frac{v}{2L}$. What is the wavelength of the sound wave?

Correct A. \frac{2L}{v}

B. \frac{v}{2L}

C. \frac{L}{v}

D. \frac{v}{L}

Correct Answer: A

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Question 11 View Details

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a speed of $v$. If the particle is subjected to a uniform magnetic field of strength $B$, what is the magnitude of the magnetic force acting on the particle?

Correct A. \frac{mv^2}{r}

B. \frac{mv^2}{2r}

C. \frac{mv^2}{4r}

D. \frac{mv^2}{8r}

Correct Answer: A

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Question 12 View Details

A body of mass $m$ is moving in a straight line with a speed of $v$. If the body is subjected to a uniform force of magnitude $F$, what is the magnitude of the acceleration of the body?

Correct A. \frac{F}{m}

B. \frac{mv^2}{F}

C. \frac{F^2}{mv}

D. \frac{mv^2}{F^2}

Correct Answer: A

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Question 13 View Details

A circuit consists of a resistor of resis\tance $R$ and an inductor of induc\tance $L$ connected in series. If the circuit is subjected to a \sinusoidal voltage source of amplitude $V_0$ and frequency $f$, what is the magnitude of the current in the circuit?

Correct A. \frac{V_0}{\sqrt{R^2 + $ 2\pi f L $^2}}

B. \frac{V_0}{R}

C. \frac{V_0}{2\pi f L}

D. \frac{V_0}{4\pi^2 f^2 L^2}

Correct Answer: A

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Question 14 View Details

A gas is heated from $T_1$ to $T_2$ at cons\tant volume. If the initial pressure is $P_1$ and the final pressure is $P_2$, what is the magnitude of the change in internal energy of the gas?

Correct A. \frac{3}{2}nR$ T_2 - T_1 $

B. \frac{5}{2}nR$ T_2 - T_1 $

C. \frac{7}{2}nR$ T_2 - T_1 $

D. \frac{9}{2}nR$ T_2 - T_1 $

Correct Answer: A

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Question 15 View Details

A radioactive sample decays with a half-life of $t_{1/2}$. If the initial activity is $A_0$ and the final activity is $A$, what is the magnitude of the decay cons\tant?

Correct A. \frac{\ln 2}{t_{1/2}}

B. \frac{t_{1/2}}{\ln 2}

C. \frac{A_0 - A}{t_{1/2}}

D. \frac{A_0 + A}{t_{1/2}}

Correct Answer: A

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Question 16 View Details

A particle of mass 2 kg is moving in a circular path of radius 3 m with a cons\tant speed of 4 m/s. If the particle is subjected to a centripetal force of 12 N, what is the magnitude of the acceleration of the particle?

A. 6 m/s^2

B. 8 m/s^2

Correct C. 10 m/s^2

D. 12 m/s^2

Correct Answer: C

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Question 17 View Details

A block of mass 5 kg is attached to a horizontal, massless spring with a force cons\tant of 200 N/m. 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

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 18 View Details

A ray 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. 25°

C. 30°

D. 35°

Correct Answer: B

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Question 19 View Details

A charged particle of mass 1 kg and charge 2 C is moving in a magnetic field of strength 0.5 T. If the particle is moving with a speed of 3 m/s, what is the magnitude of the force acting on the particle?

A. 1 N

B. 2 N

Correct C. 3 N

D. 4 N

Correct Answer: C

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Question 20 View Details

A block of mass 3 kg is moving in a straight line with a speed of 5 m/s. If the block is subjected to a force of 10 N, what is the acceleration of the block?

A. 2 m/s^2

B. 3 m/s^2

C. 4 m/s^2

Correct D. 5 m/s^2

Correct Answer: D

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Question 21 View Details

A 100 V, 50 Hz AC source is connected to a circuit containing a 20 Ω resistor and an inductor of induc\tance 0.1 H. The circuit is initially at rest. What is the maximum current in the circuit?

A. 10 A

Correct B. 20 A

C. 30 A

D. 40 A

Correct Answer: B

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Question 22 View Details

A radioactive sample has a half-life of 10 years. If the initial activity is 100 Bq, what is the activity after 20 years?

A. 50 Bq

B. 25 Bq

Correct C. 12.5 Bq

D. 6.25 Bq

Correct Answer: C

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Question 23 View Details

A 12 V battery is connected to a circuit containing a 4 Ω resistor and a 6 Ω resistor in series. What is the current in the circuit?

A. 1.5 A

Correct B. 2 A

C. 2.5 A

D. 3 A

Correct Answer: B

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Question 24 View Details

A particle of mass 2 kg is attached to a spring with a spring cons\tant of 100 N/m. The particle is displaced by 0.2 m from its equilibrium position and released from rest. What is the maximum velocity of the particle?

A. 2 m/s

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 25 View Details

A magnetic field of 0.5 T is directed along the z-axis. A current of 2 A is flowing in a wire loop of radius 0.1 m. What is the magnetic moment of the loop?

A. 0.1 A*m^2

Correct B. 0.2 A*m^2

C. 0.3 A*m^2

D. 0.4 A*m^2

Correct Answer: B

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