JAMB UTME - Physics - 2008

A sealed flask contains 600cm3 of air at 27°C and is heated to 35°C at constant pressure. The new volume is?

Answer Details

To solve this problem, we can use Charles's law, which states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature. First, we need to convert the temperatures from Celsius to Kelvin by adding 273.15: Initial temperature (in Kelvin) = 27 + 273.15 = 300.15 K Final temperature (in Kelvin) = 35 + 273.15 = 308.15 K Next, we can use the formula for Charles's law: V1 / T1 = V2 / T2 where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature. We can rearrange this formula to solve for V2: V2 = (V1 x T2) / T1 Plugging in the given values, we get: V2 = (600 cm^3 x 308.15 K) / 300.15 K V2 = 616 cm^3 Therefore, the new volume of the air in the flask is 616 cm^3.

A body of mass 4 kg resting on a smooth horizontal plane is simultaneously acted upon by two perpendicular forces 6N and 8N. Calculate the acceleration of the motion

Answer Details

To find the acceleration of the motion, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this problem, the body has a mass of 4 kg and is acted upon by two perpendicular forces of 6N and 8N. Since the plane is smooth, there is no frictional force acting on the body. Therefore, the net force acting on the body is the vector sum of the two perpendicular forces. Using the Pythagorean theorem, we can find the magnitude of the net force: Net force = sqrt((6N)^2 + (8N)^2) = 10N The direction of the net force is the angle formed between the two perpendicular forces: tan θ = (8N)/(6N) => θ = tan^-1(8/6) = 53.13° The net force is at an angle of 53.13° to the horizontal. Now, we can calculate the acceleration using Newton's second law: acceleration = net force / mass acceleration = 10N / 4kg acceleration = 2.5 ms^-1 Therefore, the acceleration of the motion is 2.5 ms^-1.

Caesium has a work function of 3 x 10-19J. the maximum energy of liberated electrons when it is illuminated by light of frequency 6.7 x 1014HZ is?

[h = 6.6 x 1010-34Js]

Answer Details

Max kinetic energy = Energy of incident electron - work function. EK = hf - w
= 6.6 x 10-34 x 6.7 x 1014 - 3 x 10-19
= 4.422 x 10-19 - 3 x 10-19
= 1.422 x 10-19J

A block of aluminum is heated electrically by a 30 w heater if the temperature rises by 10°c in 5 minutes, the heat capacity of the aluminum is

Answer Details

Heat supplied = Heat gained Pt = MCDθ
30 x 5 x 60 = c x 10
where c = mc which is the heat capacity
c = (30 x 5 x60)/10 = 900 JKg-1

If electron are accelerated from rest through a potential difference of 10kv, what is the wavelength of the associated electron

[m = 9.1 x 10-31kg, e = 1.6 x 10-19C, h = 6.6 x 10-34js]

Answer Details

The problem involves calculating the wavelength of an electron accelerated through a potential difference of 10kV, given the mass of the electron (9.1 x 10^-31 kg), the charge of the electron (1.6 x 10^-19 C), and Planck's constant (6.6 x 10^-34 Js). The formula for the wavelength of an electron is λ = h / (mv), where h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron. To find the velocity of the electron, we can use the formula for the kinetic energy of a particle, which is K = (1/2)mv^2 = eV, where K is the kinetic energy of the electron, e is the charge of the electron, and V is the potential difference through which the electron is accelerated. Solving for v, we get v = sqrt(2eV/m). Substituting the given values, we get v = 5.93 x 10^6 m/s. Finally, substituting the values of h, m, and v into the formula for the wavelength of the electron, we get λ = 1.22 x 10^-11 m, which is the first option. Therefore, the answer is: 1.22 x 10^-11 m.

The dimension of electromotive force are `

Answer Details

Electrical work W = QE,
Where Q is the quantity of change and E is the electromotive force.
∴ E = W = FxDQ_It
Where D is the displacement,I = current and t = time
But dimension of force,
= unit of mass x unit of Acceleration
= unit of mass xunit of velocityunit of time
= unit of mass x unit of displacement__unit of time x unit of time
ML/T2 = MLT-2
∴ Dimension of emf E
= MLT-2L = ML2T-3I-1__IT

The efficiency of the pulley system shown above is 80%. find the effort E required to lift the load of 1200N

Answer Details

VR = No. of pulleys = 4
Efficiency = M.A/V.R x 100% = load
Effort x 100%_V.R
∴80 = 1200 x 100 x 1100__Effort4
∴ Effort = 1200 x 100 = 375N_80 x 4

In the microscope, the eyepiece lens merely acts as?

Answer Details

The eyepiece lens in a microscope is responsible for magnifying the image produced by the objective lens. It is positioned near the viewer's eye and provides additional magnification to the already magnified image produced by the objective lens. Therefore, the eyepiece lens acts as a magnifier.

An observer with normal eyes views an object with magnifying glass of focal length 5 cm. the angular magnification is?
[least distance of distinct vision D = 25 cm]

Answer Details

When an observer views an object through a magnifying glass, the magnifying glass produces a virtual image of the object which is seen by the observer. The angular magnification is defined as the ratio of the angle subtended by the virtual image as seen through the magnifying glass to the angle subtended by the object when viewed with the unaided eye. To calculate the angular magnification, we need to first find the position of the virtual image produced by the magnifying glass. We can use the lens formula: 1/f = 1/v - 1/u where f is the focal length of the magnifying glass, u is the distance of the object from the magnifying glass, and v is the distance of the virtual image from the magnifying glass. Since the observer is viewing the object with normal eyes, the distance of the object from the observer (u) is equal to the least distance of distinct vision (D), which is given as 25 cm. Therefore, 1/0.05 = 1/v - 1/0.25 Simplifying, we get: v = 0.0667 m Now, we can calculate the angular magnification using the formula: M = -v/u where M is the angular magnification. The negative sign indicates that the image is inverted. Substituting the values, we get: M = -0.0667/0.25 = -0.2668 Therefore, the angular magnification is approximately -0.27, which is equivalent to -6 (since magnitudes are usually expressed as positive numbers). So, the answer is (A) -6.

I. Total internal reflection of light.

II. Conservation of light energy.

III. Relative motion of the earth, sun and moon.

IV. Rectilinear propation of light.

Which of the above is a phenomenon of total solar eclipse?

Answer Details

Due to rectilinear propagation of light we have ecslipse which occur as a result relative motion of the earth, sun and moon

A force F required to keep a 5 kg mass moving round a cycle of radius 3.5 m at a speed of 7 ms-1. What is the speed, if the force is tripled?

Answer Details

The force which is centripetal
F = MV2_R
=5 x 723.5
= 70
V = √(Fr) and if F is tripped, then
V = √(3Fr)/m
= √(3x70x3.5)/5
= 12.1ms-1

The diagram above is the heating curve for a solid QR is the

Answer Details

At melting point there is no change temperature

A short chain is sometimes attached to the back of a petrol tanker to?

Answer Details

A short chain is sometimes attached to the back of a petrol tanker to ensure the balancing of the tanker. Petrol tankers are designed to carry large volumes of liquid, and when the tank is partially filled, the liquid inside can slosh around and cause the tanker to become unbalanced. This can be dangerous, particularly when driving around corners or on uneven roads. The short chain is attached to the back of the tanker and hangs down towards the ground. As the tanker moves, the chain swings back and forth, creating a force that helps to counteract the sloshing of the liquid inside the tanker. This helps to keep the tanker balanced and prevents it from tipping over, which could cause a serious accident. It's important to note that the other options listed are not correct. A short chain does not generate more friction, caution the driver when overspeeding, or conduct excess charges to the car.

The resultant of two forces 12N and 5N is 13N. What is the angle between the two forces?

Answer Details

To find the angle between two forces, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the angle between them. In this case, the two forces are the other two sides of the triangle, and the resultant force is the side whose length we know. Let's call the angle between the two forces θ. Using the law of cosines, we have: 13^2 = 12^2 + 5^2 - 2(12)(5)cosθ 169 = 144 + 25 - 120cosθ cosθ = (169-144-25)/(-2*12*5) = -1/8 Since cosine is negative, the angle θ must be in the second or third quadrant (where cosine is negative). To find the angle, we can take the inverse cosine (also known as arccosine) of -1/8: θ = arccos(-1/8) ≈ 100.19 degrees Therefore, the angle between the two forces is approximately 100.19 degrees. This is closest to the third option, which is 90 degrees.

The thermometric properties of a thermocouple is the change in?

Answer Details

The thermometric properties of a thermocouple refer to the change in the electromotive force (EMF) that the thermocouple produces when exposed to different temperatures. A thermocouple consists of two wires made of different metals that are joined together at both ends to form two junctions. When one junction is exposed to a higher temperature than the other, a temperature difference is created, which generates a voltage or electromotive force (EMF) across the two junctions. The amount of EMF generated by a thermocouple is directly proportional to the temperature difference between the two junctions. Therefore, by measuring the EMF produced by a thermocouple, we can determine the temperature difference and hence the temperature at the hot junction. In summary, the thermometric properties of a thermocouple are related to the change in the electromotive force it produces when exposed to different temperatures. Therefore, the correct answer is "electromotive force".

An object 4 cm high is placed 15 cm from a concave mirror of focal length 5 cm. The size of the image is

Answer Details

This is a problem from optics involving the use of a concave mirror. When an object is placed in front of a concave mirror, the image formed can be real or virtual, depending on the position of the object relative to the mirror. In this problem, we are given the height and distance of the object from the mirror, as well as the focal length of the mirror. To find the size of the image, we need to first determine the distance of the image from the mirror. We can use the mirror equation, which relates the object distance (u), image distance (v), and focal length (f) of a mirror: 1/f = 1/v + 1/u Plugging in the given values, we get: 1/5 = 1/v + 1/15 Solving for v, we get v = 7.5 cm. Now that we know the distance of the image from the mirror, we can use similar triangles to find the size of the image. The height of the image (h') is related to the height of the object (h) by the magnification equation: h'/h = -v/u where the negative sign indicates that the image is inverted. Plugging in the values we have, we get: h'/4 = -(7.5/15) Solving for h', we get h' = 2 cm. Therefore, the size of the image is 2 cm.

The diagram above shows a plank RS pivoted its center of gravity O and is in equilibrium with the weight P and Q. If a weight 2P is added to P the plank will be in equilibrium again by

Answer Details

The plank is in equilibrium because the weight of P and Q are balanced by the weight of the plank itself, which is acting downwards through its center of gravity O. When a weight 2P is added to P, the equilibrium of the plank will be disturbed, and it will tilt downwards on the side where the weight has been added. To restore equilibrium, the weight of 2P must be balanced by an equal and opposite weight on the other side of the pivot. This can be achieved by moving Q nearer to O. By doing so, the weight of Q acting downwards through the center of gravity O will increase, and the plank will tilt back up, restoring equilibrium. The other options listed are not correct. Moving P nearer to O or adding a weight Q to Q would not restore equilibrium, as they would not provide the necessary counterbalancing weight to balance 2P. Moving P further away from O would also not work, as it would increase the weight acting downwards on that side of the pivot, making the plank tilt even further in that direction.

An electric generator has e.m.f. of 240 V and an internal resistance of 1Ω if the current supplied by the generatoris 20A when the terminal voltage is 220 V, find the ratio of the power supplied to the power dissipated?

Answer Details

Power supplied = IE = 20 X 240 = 4800 W
Power dissipated = IV = 20 X 220 = 4400 W
(Power supplied)/Power dissipated = (4800 W)/4400 W
= (12)/11

In the hare's apparatus, water rises to a height of 26.5 cm in one limb. if a liquid rises to a height of 20.4 cm in the other limb, what is the relative density of the liquid?

Answer Details

hlpl = hwpw
where, L =liquid and W = water
(pl)/pw = (hw)/hl = (26.5)/20.4
= 1.299

Find the effective resistance in the diagram above

Answer Details

In the given diagram, resistors R1 and R2 are in parallel and their equivalent resistance can be calculated as follows: 1/Req = 1/R1 + 1/R2 1/Req = 1/6Ω + 1/6Ω = 2/6Ω Req = 3Ω Resistor R3 is in series with the combination of resistors R1 and R2. Thus, the total resistance of the circuit can be calculated as follows: Rtotal = R3 + Req Rtotal = 6Ω + 3Ω = 9Ω Therefore, the effective resistance in the given diagram is 9Ω. Option (D) is correct.

A spring of force constant 500 NM-1 is compressed such that its length shortens by 5cm. The energy stored in the spring is?

Answer Details

The energy stored in a spring that has been compressed or stretched is given by the formula: E = (1/2)kx^2 where E is the energy stored, k is the spring constant, and x is the distance that the spring is compressed or stretched from its equilibrium position. In this case, the spring has a force constant of 500 Nm^-1 and is compressed by 5 cm or 0.05 m. Therefore, the energy stored in the spring is: E = (1/2)(500 Nm^-1)(0.05 m)^2 = 0.625 J Therefore, the energy stored in the spring is 0.625 J.

I. for current amplification.II. for voltage stabilization. III. for power amplification.IV. as a switch.which of the above are the uses of transistor?

Answer Details

Transistor is used for amplification of current, power and as a switch in logic gates.

I. All the three forces must be concurrent.

II. The upward force is equal to the downward force.

III. The algebraic sum of the moment about any point must be zero.which of the above conditions must hold for a body acted upon by a system of three coplanar forces equilibrium?

Answer Details

Option ii is one of the condition of an equilibrium of parallel forces only i and iii are correct

An object of height 4cm is placed in front of a cuboid pinhole camera of size 6 cm. if the image formed is 2 cm high, how far is the object from the pinhole?

Answer Details

The pinhole camera follows the basic principles of optics, where light rays coming from an object pass through a small hole and form an inverted image on the opposite side of the hole. In this case, we have an object of height 4cm placed in front of a cuboid pinhole camera of size 6 cm, and an image of height 2 cm is formed. Using similar triangles, we can determine the distance of the object from the pinhole. Let's denote this distance as 'x'. Since the image is inverted, we can say that the height of the object '4' is to the height of the image '2' as the distance of the object 'x' is to the distance of the image '6'. Therefore, we can write: 4/2 = x/6 Simplifying this equation, we get: x = 6 * 4/2 = 12 cm So, the object is placed 12 cm away from the pinhole camera. Therefore, the correct answer is 12.0 cm.

The d.c generator has essentially the same components as the a.c generator except the presence of?

Answer Details

The statement is talking about the components of a DC generator, which is a device that converts mechanical energy into electrical energy. It says that a DC generator has the same components as an AC generator, which is a device that generates alternating current (AC) electricity, except for the presence of one specific component. The component that is absent in the DC generator is the slip-ring, which is present in the AC generator. Slip-rings are used to transfer electrical power from a rotating part (such as the rotor in a generator) to a stationary part (such as the stator), while still allowing the rotating part to spin freely. In a DC generator, however, the electrical power is transferred through the use of carbon brushes that make contact with a split-ring commutator mounted on the armature. So, the answer is "slip-ring".

zener diode is used for?

Answer Details

A zener diode is a type of diode that is designed to operate in the reverse breakdown region of its voltage-current characteristic curve. In simpler terms, it is a diode that allows current to flow in the reverse direction when a certain voltage threshold is reached. This characteristic makes it useful for voltage regulation applications. When used in a circuit, a zener diode can maintain a nearly constant voltage across its terminals, even if there are changes in the input voltage or load resistance. Therefore, the correct option is "voltage regulation".

An object placed at the bottom of a well full of clear water appears closer to the surface due to?

Answer Details

Real depth and apparent dept is due to refraction

During summer, the balance wheel of a clock expands.what effect does this have on the accuracy of the clock?

Answer Details

The balance wheel of a clock is a small metal wheel that oscillates back and forth to regulate the movement of the clock. When the balance wheel expands due to the heat of summer, its period or time of oscillation increases. As a result, the clock will run slower and lose time. Therefore, the correct answer is that the clock loses time.

When a pure semiconductor is heated, its resistance

Answer Details

When a pure semiconductor is heated, its resistance decreases. This is because when the temperature of the semiconductor increases, the number of free electrons and holes also increases, which leads to an increase in the conductivity of the material. The increase in conductivity causes a decrease in the resistance of the semiconductor. The relationship between temperature and resistance of a semiconductor is described by the equation: R = Ro exp(T/Tref), where R is the resistance, Ro is the resistance at a reference temperature Tref, and T is the absolute temperature. Therefore, as the temperature increases, the value of R decreases.

When cold water is poured on a can containing hot water, the can collapses because the

Answer Details

When hot water is kept in a can and cold water is poured over it, the can collapses because of the difference in temperature of the hot water inside the can and the cold water outside the can. The metal of the can contracts due to the cooling of the hot water inside. As a result, the pressure inside the can decreases, and the external air pressure becomes greater than the pressure inside the can. This causes the can to collapse inward. Therefore, the correct option is "external pressure becomes greater than the pressure within the can."

In the equation above, the particles X is

Answer Details

for the conversion of mass 14 + 4 = 17 + x
∴ X = 18 - 17 = 1
for conservation pf charge:7 + 2 = 8 + y
y = 9 - 8 = 1
Thus, the element is 11X which is equal to hydrogen nucleus ( proton)

What is the frquency of vibration if the balance wheel of a wrist watch makes 90 revolutions in 25 s?

Answer Details

The frequency of vibration can be calculated using the formula: frequency = number of revolutions/time taken In this case, the balance wheel of a wrist watch makes 90 revolutions in 25 seconds. So, the frequency can be calculated as: frequency = 90/25 frequency = 3.6 Hz Therefore, the frequency of vibration is 3.6 Hz. Option D, "3.60 Hz", is the correct answer.

I. Force (N)

II.Torque (NM)

III. Current (A)

IV. Power (W)

Which of the above are the correct S. I: units of the quantities indicated?

Answer Details

The correct SI units for the given quantities are: I. Force - Newton (N) II. Torque - Newton meter (Nm) III. Current - Ampere (A) IV. Power - Watt (W) Therefore, the options that include the correct SI units for all the given quantities are "I, II and III only" and "I, III and IV only". It's important to note that SI units are the standard units of measurement used in science and engineering to ensure consistency and accuracy in the reporting of data. It's crucial to use the correct units of measurement to ensure that calculations are accurate and meaningful.

An empty density bottle weighs 2 N. if its weighs 5 N when filled with water and 4 N when filled with olive oil, the relative density of olive oil is

Answer Details

relative density = (weight of substance )/weight of equal volume of water = (4 - 2)/5 - 2 = (2)/3

If a wheel 1.2 m in diameter rotates at one revolation per second, calculate the velocity of the wheel.

Answer Details

To calculate the velocity of the wheel, we need to know the distance it covers in one revolution and the time taken to complete one revolution. Since the diameter of the wheel is given as 1.2 m, its radius is 0.6 m (half of the diameter). The distance covered in one revolution (circumference) = 2 x π x radius = 2 x π x 0.6 m = 1.2 x π m. The time taken to complete one revolution is given as one second. Hence, the velocity of the wheel = distance/time = (1.2 x π m) / (1 s) ≈ 3.77 ms^-1. Therefore, the answer is 3.77 ms^-1.

Convex mirror are used as driving mirrors because images formed are?

Answer Details

Image formed by convex mirror is always erect, virtual and diminished

Which of the following is NOT a vector quantity?

Answer Details

Altitude is just a measure of height, regardless of direction.

If the partial pressure of water vapour at 27°C is 18 mm Hg and the saturated vapour pressure of the atmosphere at the same temperature is 24 mm Hg, the relative humidity at this temperature is?

Answer Details

Relative humidity is the ratio of the actual amount of water vapor present in the air to the maximum amount of water vapor the air can hold at a given temperature. It is usually expressed as a percentage. In this question, the partial pressure of water vapor in the air is 18 mm Hg, and the saturated vapor pressure of the atmosphere at the same temperature is 24 mm Hg. To find the relative humidity, we need to compare the partial pressure of water vapor in the air to the saturated vapor pressure of the atmosphere at the same temperature. The ratio of the two pressures is: Relative humidity = (partial pressure of water vapor / saturated vapor pressure) x 100% Substituting the values given in the question, we get: Relative humidity = (18 mm Hg / 24 mm Hg) x 100% = 0.75 x 100% = 75% Therefore, the relative humidity at this temperature is 75%. The correct option is C.

In a good thermos flask, the main cause of heat loss is?

Answer Details

Since the cork is in contact with the walls of the flask, little conduction takes place

The above figure shows the motion of a progressive wave along a string. The particle motion of the medium is in direction

Answer Details

The particle motion of the medium in a progressive wave is perpendicular to the direction of wave propagation. In the given figure, the wave is propagating along the x-axis (OX), so the particle motion of the medium is in the direction perpendicular to OX, which is the y-axis (OY). Therefore, the answer is "parallel to OY".

A step-down transformer has a power output of 50 W and efficiency of 80%. if the mains supply voltage is 200 v, calculate the primary current of the transformer.

Answer Details

The formula for calculating the primary current of a transformer is: Primary current = (Power output / Mains voltage) / Efficiency Where the power output is given as 50 W, the mains voltage is given as 200 V, and the efficiency is given as 80% or 0.8. Substituting these values in the formula, we get: Primary current = (50 / 200) / 0.8 Primary current = 0.3125 A or 0.31 A (rounded to two decimal places) Therefore, the primary current of the transformer is 0.31 A.

A generator is on daily use and in the process, ten 60 W and five 40 W tungsten bulbs are on for the same time interval. the energy consumed daily is?

Answer Details

Energy consumed = power x time
= (60 W x 10 + 40 W x 5) x 24 h
= (600 W + 200 W ) x 24 h
= 800 W x 24h = 19200 w h
= 19.2 kWh

The fundamental property of a propagating wave which depends only on the source and not the medium of propagation is the?

Answer Details

Timber/ quality depends on the overtones or harmonics, and timber is a characteristic property of source of sound.

Counting of currency notes with moist fingers is based on the principles of?

Answer Details

Counting of currency notes with moist fingers is based on the principle of adhesion. Adhesion is the tendency of dissimilar particles or surfaces to cling to one another. When currency notes are moistened, the water molecules adhere to the surface of the paper and increase the friction between the notes, making them easier to separate and count. The same principle is used when licking the tip of a finger to turn the pages of a book. The moisture adheres to the page, allowing for better grip and separation.

If a body mass 5kg is thrown vertically upwards with velocity u,at what height will the potential energy equal to the kinetic energy?

Answer Details

The correct answer is: h = (u)2/2g. When an object is thrown vertically upwards, it rises to a certain height, reaches its maximum height, and then falls back to the ground. At the maximum height, the potential energy of the object is equal to its kinetic energy. The potential energy of an object is given by the formula: P.E = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground. The kinetic energy of an object is given by the formula: K.E = (1/2)mu^2, where m is the mass of the object, and u is the velocity of the object. At the maximum height, the velocity of the object becomes zero. Therefore, we can equate the potential energy at the maximum height to the kinetic energy just before the object reached the maximum height. So, we have: P.E = K.E mgh = (1/2)mu^2 h = (1/2)u^2/g Substituting the given values, we get: h = (u)^2/2g Therefore, the height at which the potential energy of the object is equal to its kinetic energy is given by the formula: h = (u)^2/2g.

A motorcycle of mass 100kg moves round in a circle of radius 10m with a velocity of 5 ms-1. find the coefficient of friction between the road and the tyres.

Answer Details

F = (mv)2/r = (100 x 5)2 = 250N
R = mg = 100 x 10 - 1000N
coefficient of friction,
µ = (F)/R = (250)/1000 = 0.25

If a convex lens of focal length 12cm is used to produce a real image four times the size of the object, how far from the lens must the object be placed?

Answer Details

Magnifications = V/U = 4
∴ V = 4U
1/V + 1/U = 1/f1/4u + 1/U = 1/125/4U = 1/12
4U = 12 x 5 = 60
∴ U = 15 cm

Given the inductor of inductance 5mH, 10mH and 20mH connected in series, the effective inductance is

Answer Details

When inductors are connected in series, the total inductance is the sum of the individual inductances. Therefore, the effective inductance of the inductors of inductance 5mH, 10mH, and 20mH connected in series is: Effective inductance = 5mH + 10mH + 20mH = 35mH So, the correct answer is 35.0mH. In summary, when inductors are connected in series, the total inductance is the sum of the individual inductances.

Given the progressive wave equation y = 5 sin (2000 πt - 0.4x), calculate wave length

Answer Details

In the equation y = 5 sin (2000 πt - 0.4x), the term inside the sine function (2000 πt - 0.4x) represents the phase of the wave, which should be constant for a given wave. The wavelength (λ) is the distance between two consecutive points in the wave that are in phase with each other. To find the wavelength, we need to isolate the term that represents the distance between two consecutive points in phase. In this case, that term is -0.4x, which is the coefficient of the x variable. We know that the wavelength is given by the formula λ = 2π/k, where k is the wave number, which is equal to the coefficient of the x variable. So, we have k = -0.4. Plugging this value into the formula for wavelength gives λ = 2π/-0.4 ≈ 15.7 meters. Therefore, the wavelength of the wave is 15.7 meters.

An object of heights 5 cm is placed at 20 cm from a concave mirror of focal length 10 cm. the image height is?

Answer Details

The problem involves a concave mirror and an object placed in front of it. We are given that the object height is 5 cm, and the object is placed at a distance of 20 cm from the mirror, which has a focal length of 10 cm. To find the image height, we can use the mirror formula: 1/f = 1/v + 1/u where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. We can rearrange the formula to solve for v: 1/v = 1/f - 1/u Substituting the given values, we get: 1/v = 1/10 - 1/20 Simplifying: 1/v = 1/20 v = 20 cm This means that the image is formed at a distance of 20 cm behind the mirror. Now, we can use the magnification formula: m = -v/u where m is the magnification of the image. Substituting the given values, we get: m = -20/20 = -1 The negative sign indicates that the image is inverted. Finally, we can use the formula for image height: hi = -m * ho where hi is the height of the image, and ho is the height of the object. Substituting the given values, we get: hi = -(-1) * 5 = 5 cm Therefore, the image height is 5 cm, which is the same as the height of the object. So, the correct answer is: 5 cm.