JAMB UTME - Physics - 2017

The S.I unit of moment of a force is

Détails de la réponse

Moment of a force is the product of a force and the perpendicular distance from the line of action of the force
Moment = force × distance
= N × m
= Nm

Calculate the angle of minimum deviation of a 60o prism of a refractive index [sin-10.75 = 49o]

Détails de la réponse

For a refractive index () = $\frac{\sin \frac{1}{2}(A+D)}{\sin \frac{1}{2}A}$

D = angle of minimum deviation

A = refractive angle of the prism

1.5 = $\frac{\sin \frac{1}{2}(60+D)}{\sin \frac{1}{2}\times 60}$

1.5 = $\frac{\sin \frac{1}{2}(60+D)}{\sin 30}$

Sin $\frac{1}{2}$ (60 + D) = 1.5 * Sin 30

Sin $\frac{1}{2}$ (60 + D) = 0.75

$\frac{1}{2}$ (60 + D) = Sin-1 (0.75)

but Sin-1 (0.75) = 49o

$\frac{1}{2}$ (60 + D) = 49

60 + D = 2 * 49 = 98o

D = 98o - 60o

D = 38o

Which is the incorrect formula for a body accelerating uniformly?

Détails de la réponse

s = $\frac{1}{2}$ut + at2 is a wrong equation, it should be s = ut + $\frac{1}{2}$at2

The thermal expansion of a solid is an advantage in

Détails de la réponse

Thermal expansion of a solid is majorly advantageous in the use of bimetallic strip in the balance of a watch so as not to lose time

From the diagram above, calculate the energy stored in the capacitor

Détails de la réponse

c = 8µF, v = 10v

Energy stored = $\frac{1}{2}$ cv2

= $\frac{1}{2}$ × (8 × 10− 6) × 102

= 4 × 10${}^{-4}$

What is the speed of a body vibrating at 50 cyclic per second

Détails de la réponse

1 cycle = 3600 = 2? rad

? 50 cycle = 2 ? rad × 50 = 100 ?rad

? = angular speed = 50 cycles per seconds = 100 ? rads${}_{?1}$

Why do soldiers march disorderly while crossing a bridge?

Détails de la réponse

Soldiers march disorderly while crossing a bridge to prevent resonance because when soldiers march in orderly manner across a bridge, they generate a rhythmic oscillation of wave out. The bridge and at a certain point, would start oscillation to the same rhym as that of the marching steps. This oscillation would reach a maximum peak when the bridge can no longer sustain its own strength and hence collapses. So for this reasons, soldier are ordered to march disorderly while crossing a bridge

When the r.m.s value of a source of electricity supply is given as 240v, it means that the peak value of the supply is

Détails de la réponse

When the r.m.s value of a source of electricity supply is given as 240V, it means that the peak value of the supply is about 340V. The root-mean-square (r.m.s) value of an AC voltage or current is a way to express the effective or average value of that signal. In the case of a sine wave, the r.m.s value is approximately 0.707 times the peak value of the wave. So, to calculate the peak voltage of a 240V r.m.s supply, we can divide the r.m.s value by 0.707. Using this formula, the peak value of a 240V r.m.s supply can be calculated as: Peak value = r.m.s value / 0.707 = 240V / 0.707 ≈ 339.6V Therefore, the peak value of the supply is approximately 340V. It is important to note that this formula assumes a perfect sine wave, and in reality, the peak value of a voltage signal can fluctuate depending on various factors.

Calculate the specific latent heat of vaporization of steam of 1.13 x 106J pf heat energy is required to convert 15kg of it to water.

Détails de la réponse

The specific latent heat of vaporization of steam is the amount of heat energy required to convert one kilogram of water into steam at a constant temperature. The given problem states that 1.13 x 106 J of heat energy is required to convert 15 kg of steam to water. We can use the formula: heat energy = mass x specific latent heat where the mass is 15 kg and the heat energy is 1.13 x 106 J. Rearranging the formula, we get: specific latent heat = heat energy / mass Substituting the values, we get: specific latent heat = 1.13 x 106 J / 15 kg = 7.53 x 104 J/kg Therefore, the specific latent heat of vaporization of steam is 7.53 x 104 J/kg. The correct option is (3): 7.53 x 104 J/kg-1.

Which of the following is a semiconductor

Détails de la réponse

The semiconductor among the given options is "silicon." Semiconductors are materials that have electrical conductivity between that of a conductor and an insulator. They are widely used in electronics, such as in the construction of computer chips. Copper is a good conductor of electricity and is commonly used in electrical wiring. It is not a semiconductor. Silicon, on the other hand, is one of the most commonly used semiconductor materials in the electronics industry. It has four valence electrons, which allow it to form a crystal lattice structure with other silicon atoms. This structure gives silicon its unique electrical properties that make it useful in electronic devices such as transistors and solar cells. Plastic and iron are not semiconductors. Plastic is an insulator, which means it does not conduct electricity at all, while iron is a conductor, like copper, and does not exhibit the unique electrical properties of a semiconductor.

Which of the following is not an electromagnetic radiation?

Détails de la réponse

The answer is: sound waves is not an electromagnetic radiation. Electromagnetic radiation is a type of energy that travels through space at the speed of light in the form of waves. It is made up of oscillating electric and magnetic fields, and it includes a wide range of phenomena such as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays, and gamma rays. Sound waves, on the other hand, are not electromagnetic radiation. They are mechanical waves that require a medium to travel through, such as air, water, or solids. When an object vibrates, it creates sound waves that travel through the medium and can be heard by our ears. So, while x-rays, radio waves, and sunlight are all examples of electromagnetic radiation, sound waves are not.

Three 3ω resistance are connected in parallel what is the equivalent resistance?

Détails de la réponse

Resistor connected in a parallel have an equivalence given by
$\frac{1}{\text{Reff}}$ = $\frac{1}{3}$ + $\frac{1}{3}$ + $\frac{1}{3}$

= $\frac{1+1+1}{3}$ = $\frac{3}{3}$ = 1

Reff = 1ω

When two mirrors are placed at an angle of 900 to each other, how many images will be formed when an object is placed in front of the mirrors

Détails de la réponse

When two mirror are inclined at an angle θ, the number of images formed, n = $\frac{360}{\theta }$ − 1

∴ since $\theta$ = 90o

∴ $\frac{360}{\theta }$ − 1

= 4 − 1

= 3

The instrument to measure the relative density of light is

Détails de la réponse

The instrument used to measure the relative density of light is a hydrometer. A hydrometer is a device that is designed to measure the density of a liquid by comparing it to the density of water. In order to measure the relative density of light, the hydrometer is placed in a liquid with a known density, such as water. The hydrometer will float at a certain level in the liquid, which indicates the density of the liquid. When measuring the relative density of light, the hydrometer is placed in a liquid that has been made less dense by the addition of a solute, such as sugar or salt. The hydrometer will float at a higher level in the less dense liquid, indicating that the relative density of the light is lower than that of the liquid without the solute. In summary, a hydrometer is the instrument used to measure the relative density of light by comparing it to the density of a liquid with a known density, such as water.

A cell of internal resistance 2 π supplies current to a 6 π resistor. The efficiency of the cell is

Détails de la réponse

Internal resistance determine the maximum current that can be supplied

Efficiency = $\frac{r}{R}$ × 100

= $\text{frca}26$ × 100

= 33.3%

A constant force of 5N acts for 5 seconds on a mass of 5kg initially at rest. Calculate the final momentum

Détails de la réponse

Impulse = momentum

Impulse = Force (f) × time (t)

Momentum = mass (m) × velocity (v)

? Ft = Final momentum - initial momentum

FT = mv - mu

Since it is initially at rest u = 0

? 5 × 5 = mv ? m(0)

25 = mv

? Final momentum = 25kgms${}^{?1}$

Which of the following instruments helps to maintain the correct humidity and temperature of a building?

Détails de la réponse

The instrument that helps to maintain the correct humidity and temperature of a building is an air conditioner. An air conditioner works by removing heat and moisture from the air inside a building, and then circulating cooled and dehumidified air back into the room. It uses a refrigerant to cool the air, and a fan to circulate it. This helps to maintain a comfortable indoor temperature and humidity level, even during hot and humid weather conditions.

Calculate the electric field intensity between two plates of potential difference 6.5V when separated by a distance of 35cm.

Détails de la réponse

The electric field intensity E between two parallel plates of potential difference V separated by a distance d is given by E = V/d. Substituting the given values, we have E = 6.5V/0.35m = 18.57 NC^−1. Therefore, the electric field intensity between the two plates is 18.57 NC^−1. Answer: 18.57NC^−1

Calculate the upthrust on an object of volume 50cm3 which is immersed in liquid of density 103kgm-3 [g = 10ms-2]

Détails de la réponse

To calculate the upthrust on an object immersed in a fluid, we need to use Archimedes' principle which states that the upthrust (buoyant force) experienced by an object partially or fully submerged in a fluid is equal to the weight of the fluid displaced by the object. First, let's convert the volume of the object into meters cubed: 50 cm^3 = (50/100)^3 m^3 = 0.0005 m^3 The weight of the liquid displaced by the object is: density of liquid x volume of liquid displaced x acceleration due to gravity = 103 kg/m^3 x 0.0005 m^3 x 10 m/s^2 = 0.515 N Therefore, the upthrust (buoyant force) acting on the object is 0.515 N. So, the correct answer is option C: 0.5N.

A radio station broadcast at a frequency of 600KHZ. If the speed of light in air is 3 × 108ms${}^{-1}$. Calculate the wavelength of the radio wave

Détails de la réponse

The formula to calculate the wavelength of a wave is: wavelength = speed of light / frequency where wavelength is the distance between two consecutive peaks or troughs of a wave, frequency is the number of cycles of the wave per second, and the speed of light in air is approximately 3 × 10^8 m/s. In this question, the frequency of the radio wave is given as 600 kHz, which means that it has 600,000 cycles per second. Substituting these values into the formula, we get: wavelength = 3 × 10^8 m/s / 600,000 s^-1 wavelength = 500 m Therefore, the wavelength of the radio wave is 500 meters. The answer is: 5.0 × 10^2 m.

Under what conditions are cathode rays produced in a discharge tube?

Détails de la réponse

Cathode rays are streams of electrons that are emitted from the cathode of a discharge tube. A discharge tube is a partially evacuated glass tube with two metal electrodes: a cathode (negative electrode) and an anode (positive electrode). When a voltage is applied across the electrodes, a current flows through the gas in the tube, and cathode rays can be produced. The conditions required to produce cathode rays in a discharge tube are low pressure and high voltage. When the gas inside the tube is at a low pressure, there are fewer gas molecules to collide with the electrons emitted from the cathode. This means that the electrons can travel a longer distance without colliding with other particles, which allows them to form a visible beam of cathode rays. The high voltage applied to the electrodes causes a potential difference between the cathode and anode. This potential difference accelerates the electrons emitted from the cathode towards the anode. The faster the electrons travel, the more kinetic energy they have, and the more likely they are to collide with other gas molecules in the tube. These collisions can cause the gas molecules to become ionized, which can create a cascade effect, leading to the production of more electrons and the formation of a bright beam of cathode rays. Therefore, the correct answer is: Low pressure and high voltage.

Which of the following is correct about an electric cell?

Détails de la réponse

About electric cell
Primary cells are used up gradually often the cells are use and it can't be recharged
Secondary cells or accumulated can be recharged and used for a long period of time and their main advantage is that they have low internal resistance

A string of length 5cm is extended by 0.04m when a load of 0.8kg is suspended at the end. How far will it extend if a force of 16N is applied? [g = 10ms${}^{-2}$]

Détails de la réponse

The extension of a string when a load is suspended from it is given by Hooke's Law which states that the extension is proportional to the force applied. The proportionality constant is called the spring constant, represented by k. Mathematically, we can express this relationship as: F = kx where F is the force applied, x is the extension, and k is the spring constant. To solve this problem, we need to find the spring constant, k, of the string. We can use the information given in the problem to calculate k as follows: k = F/x where F is the force applied and x is the extension. We are given that the string of length 5cm (which is 0.05m) is extended by 0.04m when a load of 0.8kg is suspended at the end. We can convert the mass to force using the formula F = mg, where g is the acceleration due to gravity (g = 10ms^-2). F = 0.8kg × 10ms^-2 = 8N Using the formula for the spring constant, we get: k = F/x = 8N / 0.04m = 200N/m Now, we can use this spring constant to find the extension when a force of 16N is applied. Again, we can use the formula F = kx and rearrange it to solve for x: x = F/k Plugging in the values, we get: x = 16N / 200N/m = 0.08m Therefore, the string will extend by 0.08m when a force of 16N is applied. The answer is (D) 0.08m.

A man of mass 50kg ascends a flight of stains 5m high in 5 seconds. If acceleration due to gravity is 10ms${}^{-2}$ the power expended is

Détails de la réponse

To find the power expended, we can use the formula: power = force × velocity Since the man is ascending the stairs at a constant speed, the net force acting on him is zero. However, he is working against the force of gravity, which is pulling him downward with a force equal to his weight, given by: force = mass × acceleration due to gravity = 50 kg × 10 m/s^2 = 500 N The velocity of the man can be found from the distance he covers and the time taken: velocity = distance/time = 5 m/5 s = 1 m/s Thus, the power expended by the man is: power = force × velocity = 500 N × 1 m/s = 500 watts Therefore, the correct answer is option D: 500w.

Which of the following is not a mechanical wave?

Détails de la réponse

Radio waves are not a mechanical wave. Mechanical waves are waves that require a medium to propagate, meaning they can only travel through a physical material. Examples of mechanical waves include sound waves, water waves, and waves in a closed pipe. Radio waves, on the other hand, are electromagnetic waves and do not require a medium to propagate. They can travel through a vacuum, such as space, and are used for communication technologies like radio and television broadcasting, cell phone signals, and GPS.

A block and tackle pulley arrangement has 6 pulleys in which an effort of 50N supports a load of 200N, calculate the efficiency of the machine

Détails de la réponse

Which of the following representations is correct for an atom X with 28 electrons and 30 neutrons?

Détails de la réponse

An atom can be represented thus,

${}_A^{Z}X$ where Z = mass number

A = atomic number

A = number of proton = number of electrons in a free state = 28

Z = number of protons + number of neutrons = 28 + 30 = 58

${}_{28}^{58}X$is the representation

Determine the focal length of a thin converging lens if the power is 5.0 dioptres

Détails de la réponse

The formula for calculating the focal length (f) of a thin converging lens in meters using its power (P) in dioptres is: f = 1/P In this problem, the power of the lens is given as 5.0 dioptres. So, substituting this value in the above formula, we get: f = 1/5.0 = 0.2 meters Therefore, the focal length of the lens is 0.2 meters (or 20 centimeters). This means that when parallel light rays pass through this lens, they will converge to a point that is 0.2 meters (20 centimeters) away from the lens. The smaller the focal length of a lens, the greater its ability to converge light, and the stronger its power. So, the correct answer is 0.2 m.

Calculate the light of the image formed by a pinhole camera of length 12cm used to photograph an object 60cm away from the hole and 70cm high

Détails de la réponse

Magnification = $\frac{\text{Length of camera}}{\text{distance of object from pin hole}}$

m = $\frac{12}{60}$

= 0.2

Also magnification m = $\frac{\text{Height of image}}{\text{Height of object}}$

∴ Height of image = m × height of object

= 0.2 × 70

= 14cm

Which of the following statements is NOT correct?

Détails de la réponse

The correct answer is "Molecules of a liquid are stationary" is not correct. This statement is incorrect because the molecules of a liquid are not stationary, they are in constant motion. The molecules in a liquid are able to move past each other, which is why liquids can take the shape of their container. The other statements are all correct. Matter is indeed made up of molecules, and the constant motion of these molecules is what gives matter its physical properties. Brownian motion, which is the random movement of particles in a fluid, is a visible example of the motion of particles in matter and provides evidence for the particle nature of matter.

Which of the following is a scalar quantity?

Détails de la réponse

Scalar quantity is a quantity with only magnitude, it has no direction
Tension, weight, impulse are vector quantities because they have direction. Mass is the only scalar quantity there

The volume of a fixed mass of gas is 10cm3 when its pressure is 400cmHg. Determine the volume of the gas when its pressure is 200cmHg.

Détails de la réponse

This problem can be solved using Boyle's law, which states that the pressure of a gas is inversely proportional to its volume, as long as the temperature remains constant. Mathematically, Boyle's law can be written as: P1V1 = P2V2 where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. In this problem, we are given that the initial volume (V1) is 10cm^3 and the initial pressure (P1) is 400cmHg. We are asked to find the final volume (V2) when the pressure (P2) is 200cmHg. Using Boyle's law, we can write: P1V1 = P2V2 400cmHg x 10cm^3 = 200cmHg x V2 Solving for V2, we get: V2 = (400cmHg x 10cm^3) / 200cmHg V2 = 20cm^3 Therefore, the volume of the gas when its pressure is 200cmHg is 20cm^3. Answer option (D) is correct.

The velocity ratio of an inclined plane where angle of inclination in θ is

Détails de la réponse

Consider an inclined plane shown below, as the effort moves along OB, the load moves is lifted up through a vertical height AB

V.R = $\frac{\text{distance moved by effort}}{\text{distance moved by load}}$ = $\frac{OB}{AB}$

But Sinθ = $\frac{opp}{hyp}$ = $\frac{AB}{OB}$

therefore; = $\frac{OB}{AB}$ = $\frac{1}{\sin \theta }$

I. Refraction II. Interference III. Diffraction
Which of the above properties are common to all waves?

Détails de la réponse

The properties of refraction, interference, and diffraction are all common to all types of waves. Refraction is the bending of waves as they pass through a medium with a different density. All types of waves, including sound waves, water waves, and light waves, can refract when they encounter a medium with a different density. Interference occurs when two or more waves interact with each other. This can result in constructive interference, where the waves combine to form a larger wave, or destructive interference, where the waves cancel each other out. All types of waves can interfere with each other. Diffraction is the bending of waves around obstacles or through openings. This phenomenon can be observed when sound waves bend around a corner, or when light waves diffract through a small opening, creating a pattern of light and dark bands. All types of waves can diffract. Therefore, the correct answer is "I, II and III," as all three properties are common to all waves.

From the diagram above, calculate the total current in the circuit

Détails de la réponse

V = IR from ohms law

I = $\frac{V}{R}$

Since the resistance are in parallel

$\frac{1}{Reff}$ = $\frac{1}{8}$ + $\frac{1}{12}$ + $\frac{1}{6}$

= $\frac{2+3+6}{36}$ = $\frac{11}{36}$

Reff = $\frac{36}{11}$ = 3.27

I = I1 + I2 + I3

= $\frac{V}{Reff}$= $\frac{12}{3.27}$

= 3.669A

I = 3.7A

Under which of the following conditions is work done?

Détails de la réponse

Work Is only done when an object is moved to a distance.
The ans is C because the man pushed the table to a distance. The rest no work is done.
Ans C

The net capacitance in the circuit above is

Détails de la réponse

For capacitance i n parallel, 2µF and 2µF are in parallel,
their equivalence is 2µF and 2µF = 4µF

The 4µF generated is now in series with the remaining 4µF.

The net capacitance for series connection is

$\frac{1}{C}$ = $\frac{1}{4}$ + $\frac{1}{4}$ = 1 + $\frac{1}{4}$ = $\frac{2}{4}$

C = $\frac{4}{2}$

= 2µF

The instrument used to measure the pressure of a gas is

Détails de la réponse

Barometer is used to measure atmosphere pressure
Thermometer is used to measure temperature
Hygrometer is used to measure relative density of a liquid
Manometer is used to measure the pressure of a gas

The action of blotting paper on ink is due to

Détails de la réponse

The action of blotting paper on ink is due to capillarity. Capillarity is the ability of a liquid to flow in narrow spaces, such as the fibers of a piece of blotting paper, against the force of gravity. This is made possible because of the combination of the liquid's surface tension, which acts like a skin on the surface of the liquid, and the wicking action of the fibers in the paper. The fibers in the blotting paper wick the ink from the surface it is on, and the ink is held in the fibers due to the surface tension of the liquid. This is why blotting paper is effective in removing excess ink from surfaces, because it pulls the ink into its fibers and holds it there.

Calculate the time taken for a mango fruit that fall from the tree 20 m to the ground [g = 10 ms-2]

Détails de la réponse

To calculate the time taken for a mango fruit to fall from a tree to the ground, we can use the following formula: distance = (1/2) x acceleration x time^2 Where: distance = 20m (the height of the tree) acceleration = 10 m/s^2 (acceleration due to gravity) time = unknown (what we are solving for) Rearranging the formula, we get: time = square root(2 x distance / acceleration) Plugging in the values we get: time = square root(2 x 20 / 10) time = square root(4) time = 2 seconds Therefore, the time taken for a mango fruit to fall from a tree 20 m to the ground is 2 seconds.