Practice post utme futa physics 2017 Past Questions

Question 1

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?

A. mv^2 r / k

B. mv^2 r^2 / k

C. mv^2 r / k^2

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

Question 2

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?

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

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

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

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

Question 3

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. What is the magnitude of the force acting on the particle?

A. 8 N

B. 12 N

C. 16 N

D. 20 N

Question 4

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

A. 236

B. 238

C. 240

D. 242

Question 5

A gas is confined to a cylinder of volume $V$ with a movable piston. The gas is heated, cau\sing its pressure to increase. If the piston is initially at position $x_0$ and the gas expands to position $x_1$, what is the work done by the gas?

A. \frac{P_0 V}{x_1 - x_0}

B. \frac{P_1 V}{x_1 - x_0}

C. \int_{x_0}^{x_1} P dx

D. \frac{P_0 V}{x_1 + x_0}

Question 6

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.

A. T = 2π√$ 3ρV/Mg $

B. T = 2π√$ ρV/Mg $

C. T = 2π√$ 3ρV/M $

D. T = 2π√$ ρV/M $

Question 7

A heat engine operates between the temperatures 500 K and 300 K. If the engine absorbs 2000 J of heat from the high-temperature reservoir, what is the efficiency of the engine?

A. 0.25

B. 0.30

C. 0.35

D. 0.40

Question 8

A gas of $N$ molecules is confined to a volume $V$. The molecules are assumed to be ideal and non-interacting. What is the average kinetic energy of the molecules?

A. \frac{3}{2} NkT

B. \frac{3}{2} kT

C. \frac{1}{2} NkT

D. \frac{1}{2} kT

Question 9

A particle of mass $m$ is moving in a circular orbit of radius $r$ with a velocity $v$. What is the centripetal force acting on the particle?

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

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

C. \frac{mvr}{r}

D. \frac{mvr^2}{r}

Question 10

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 11

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 12

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

B. 20 m

C. 30 m

D. 40 m

Question 13

A gas is confined to a cylinder of volume $V$ with a movable piston. The gas is heated, cau\sing its pressure to increase. If the piston is initially at position $x_0$ and the gas expands to position $x_1$, what is the work done by the gas?

A. \frac{P_0 V}{x_1 - x_0}

B. \frac{P_1 V}{x_1 - x_0}

C. \int_{x_0}^{x_1} P dx

D. \frac{P_0 V}{x_1 + x_0}

Question 14

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

C. 1 V

D. 5 V

Question 15

A particle of mass $m$ is moving in a one-dimensional potential $V(x) = \frac{1}{2} kx^2$. If the particle is initially at rest at position $x_0$, what is its momentum at time $t$?

A. \sqrt{\frac{k}{m}} x_0 \sin \omega t

B. \sqrt{\frac{k}{m}} x_0 \cos \omega t

C. \sqrt{\frac{k}{m}} x_0 \sin \omega t \cos \omega t

D. \sqrt{\frac{k}{m}} x_0 \cos \omega t \sin \omega t

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