JAMB UTME - Physics - 2023

The pinhole camera works on

Answer Details

The pinhole camera works on the principle of the rectilinear propagation of light. This principle states that light travels in straight lines. When light passes through the tiny hole in a pinhole camera, it forms an inverted image on the opposite side of the camera. The size of the image depends on the distance between the object and the pinhole.

The sensitivity of a thermometer is

Answer Details

The sensitivity of a thermometer refers to the smallest temperature change that it can detect or measure. In other words, it measures how fine or precise the thermometer is in detecting changes in temperature. A thermometer with high sensitivity is able to detect even small changes in temperature, while a thermometer with low sensitivity may only detect larger temperature fluctuations.

Therefore, in the given options, the statement "the smallest temperature change that can be detected or measured" accurately describes the sensitivity of a thermometer.

The pitch of a musical note is determined by the frequency of the sound wave that it produces. If two instruments have the same frequency, which of the following factors will most affect the difference in their pitches?

Answer Details

The frequency of a sound wave is proportional to the tension of the string. If two instruments have the same frequency, but one has a tighter string, then the instrument with the tighter string will have a higher pitch.

The other factors listed, such as the size of the instrument, the material of the instrument, and the shape of the instrument, will also affect the pitch of the instrument, but they will have a smaller effect than the tension of the string.

Which of the following types of electromagnetic waves is used in night vision goggles?

Answer Details

Night vision goggles use infrared waves to enable the user to see in the dark.

Infrared waves are a type of electromagnetic radiation that have longer wavelengths than visible light. They fall between the visible and microwave regions on the electromagnetic spectrum. Unlike visible light, which is visible to the human eye, infrared waves cannot be seen without the use of specialized devices such as night vision goggles.

When it is dark, objects do not emit visible light that can be detected by the human eye. However, they do emit heat in the form of infrared radiation. Night vision goggles work by detecting and amplifying this infrared radiation, which is then converted into visible light that can be seen by the user.

The goggles contain an image intensifier tube that is sensitive to infrared radiation. This tube amplifies the incoming infrared light and converts it into an image that can be seen through the goggles. The resulting image appears green because the human eye is more sensitive to green light.

Therefore, to see in the dark, night vision goggles use infrared waves to detect and amplify the infrared radiation emitted by objects. This enables the user to have enhanced vision in low-light conditions or complete darkness.

A metal sphere is placed on an insulating stand. A negatively charged rod is brought close to it. If the sphere is earthed and the rod is taken away, what will be the charge on the sphere?

Answer Details

When a negatively charged rod is brought close to a metal sphere, the free electrons in the sphere are repelled from the rod and move to the other end of the sphere. This creates a region of positive charge on the side of the sphere closest to the rod, and a region of negative charge on the opposite side. The process of charge distribution stops when the net force on the free electrons inside the metal is equal to zero.

If the sphere is then earthed, the free electrons will flow from the sphere to the ground, leaving the sphere with a net positive charge.

The half life of a radioactive material is 12 days. Calculate the decay constant.

Answer Details

The decay constant of a radioactive material represents the probability that an atom of the material will decay in a unit of time. In this case, we are given the half-life of the material which is the time it takes for half of the radioactive atoms to decay.
The relationship between the decay constant (λ) and the half-life (T½) is given by the formula:
λ = ln(2) / T½
where ln(2) is the natural logarithm of 2.
To find the decay constant, we can plug in the given half-life value into the formula. In this case, the half-life is 12 days.
λ = ln(2) / 12
Using a calculator, we can calculate the value of ln(2) ≈ 0.6931.
λ = 0.6931 / 12 ≈ 0.05775 day^(-1)
Therefore, the decay constant for this radioactive material is approximately 0.05775 day^(-1).
The correct answer is 0.05775 day^(-1).

Which of the following is a type of incandescent light source?

Answer Details

The Tungsten filament lamp is a type of incandescent light source.

An incandescent light source works by using electricity to heat a filament inside the bulb until it becomes so hot that it emits light. In a tungsten filament lamp, the filament is made of tungsten, which is a metal that has a very high melting point. This allows the filament to get extremely hot without melting.

When an electric current passes through the filament, it heats up and starts to glow, producing visible light. The light emitted by a tungsten filament lamp is actually a result of the high temperature, which causes the atoms in the filament to vibrate and release energy in the form of light.

Incandescent light sources like tungsten filament lamps have been widely used for many years because they produce a warm, yellowish light that is similar to natural sunlight. However, they are not very energy-efficient, as a significant amount of the electrical energy is converted into heat rather than light.

In recent years, there has been a shift towards more energy-efficient alternatives like LED lamps and fluorescent lamps. LED lamps use a different mechanism to produce light, using a semiconductor that emits light when electric current passes through it. Fluorescent lamps use a gas-filled tube that emits ultraviolet light when electric current flows through it, and this ultraviolet light is then converted into visible light by a phosphor coating inside the tube.

So, in summary, the tungsten filament lamp is the type of incandescent light source among the options given. It works by heating a tungsten filament to a very high temperature, causing it to emit light. However, it is less energy-efficient compared to LED and fluorescent lamps.

Which of the following is/are not true about the heat capacity of a substance?
(i) It is an intensive property
(ii) Its S.I unit is jK−1
(iii) It is an extensive property
(iv) Its S.I unit is jkg−1

Answer Details

The correct answer is (ii) and (iii) only. The heat capacity of a substance is a measure of how much heat energy is required to raise the temperature of the substance by a certain amount. It is an important property in thermodynamics. (i) It is not true that heat capacity is an intensive property. Intensive properties do not depend on the size or amount of the substance. For example, density and temperature are intensive properties. However, heat capacity does depend on the size or amount of the substance. The heat capacity of a substance increases with its mass or amount. Therefore, statement (i) is false. (ii) It is true that the SI unit of heat capacity is joules per kelvin (J/K). Heat capacity is defined as the amount of heat energy (in joules) required to raise the temperature of a substance by 1 degree kelvin. Therefore, statement (ii) is true. (iii) It is not true that heat capacity is an extensive property. Extensive properties depend on the size or amount of the substance. Examples of extensive properties include mass and volume. However, heat capacity is an intensive property as explained earlier. Therefore, statement (iii) is false. (iv) It is true that the SI unit of heat capacity is joules per kilogram per kelvin (J/(kg·K)). This unit is commonly used for specific heat capacity, which is the heat capacity per unit mass. Therefore, statement (iv) is true. In summary, the correct statement is that (ii) and (iii) are not true about the heat capacity of a substance.

A parallel plate capacitor separated by an air gap is made of 0.8m2 tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate?

Take εo = 8.85 * 10-12 Fm−1

Answer Details

To calculate the charge on each plate of a parallel plate capacitor, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage applied. The capacitance of a parallel plate capacitor can be calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of the medium (in this case, air), A is the area of each plate, and d is the distance between the plates. Given: Area of each plate (A) = 0.8 m^2 Distance between the plates (d) = 20 mm = 0.02 m Permittivity of air (ε) = 8.85 x 10^-12 F/m Using the formula for capacitance, we can calculate C: C = εA/d = (8.85 x 10^-12 F/m)(0.8 m^2)/(0.02 m) = 8.85 x 10^-12 F/m * 40 F = 3.54 x 10^-10 F Now, we can use the formula Q = CV to calculate the charge on each plate: Q = (3.54 x 10^-10 F)(120 V) = 4.25 x 10^-8 C = 42.5 x 10^-9 C = 42.5 nC Therefore, the charge on each plate of the parallel plate capacitor is **42.5 nC**.

A charge of 4.6×10−5 $4.6\times {10}^{-}5$C is placed in an electric field of intensity 3.2×104 $3.2\times {10}^4$ Vm−1
. What is the force acting on the electron?

Answer Details

To calculate the force acting on the charge in an electric field, we can use the formula: F = q * E Where: F is the force acting on the charge, q is the charge of the particle, and E is the electric field intensity. In this case, the charge is given as 4.6 × 10^(-5) C and the electric field intensity is given as 3.2 × 10^4 V/m. Substituting these values into the formula: F = (4.6 × 10^(-5) C) * (3.2 × 10^4 V/m) To multiply numbers in scientific notation, we multiply the coefficients and add the exponents: F = (4.6 * 3.2) * (10^(-5 + 4)) C * V/m F = 14.72 * 10^(-1) C * V/m To simplify, we can convert the result to standard form: F = 1.472 C * V/m Therefore, the force acting on the charge is **1.472 N**.

Find the tension in the two cords shown in the figure above. Neglect the mass of the cords, and assume that the angle is 38° and the mass m is 220 kg

[Take g = 9.8 ms-2]

Answer Details

W =  mg  = 220 x 9.8 = 2156 N

⇒Sin 38º = 2156T1 $\frac{\mathrm{<br>}}{}$

⇒ T1 ${\mathrm{<br>}}_{}$ =    2156Sin38

⇒ T1 ${\mathrm{<br>}}_{}$ =     3502 N

Cos 38º =  T2T1 $\frac{{\mathrm{<br>}}_{}}{}$

⇒ T2 ${\mathrm{<br>}}_{}$  =   3502 x Cos 38º

⇒ T2 ${\mathrm{<br>}}_{}$ =   2760 N

;    T1 ${\mathrm{<br>}}_{}$ =   3502 N,  T2
 = 2760 N.

Which of the following liquids has the highest surface tension?

Answer Details

Surface tension is a property of liquids that arises due to the cohesive forces between the molecules at the surface. It can be thought of as the "skin" or "film" that forms on the surface of a liquid.

Considering the options given:

- Water: Water molecules have strong cohesive forces, allowing them to form hydrogen bonds with each other. As a result, water has relatively high surface tension.

- Mercury: Mercury is a metal with metallic bonding, which is much stronger than the cohesive forces in liquids. As a result, mercury has very high surface tension.

- Oil: Oils typically consist of nonpolar molecules, which have weaker cohesive forces compared to polar molecules like water. Therefore, oil generally has lower surface tension than water.

Based on this information, we can conclude that mercury has the highest surface tension among these liquids.

A beam of light traveling in water is incident on a glass which is immersed in the water. The incident beam makes an angle of 40o ${\mathrm{<br>}}^{}$ with the normal. Calculate the angle of refraction in the glass.

[Refractive index of water = 1.33, Refractive index of glass = 1.5]

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Which of the following statements regarding the application of electrical conduction via gases is/are correct?
Electrical conduction in gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Photocells
(iv) Cathode ray oscilloscope/T.V. tubes

Answer Details

Electrical conduction of gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Advertising industry/Neon signs
(iv) Cathode ray oscilloscope/T.V. tubes

The near point of a patient's eye is 50.0 cm. What power (in diopters) must a corrective lens have to enable the eye to see clearly an object 25.0 cm away?

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The terminals of a battery of emf 24.0 V and internal resistance of 1.0 Ω is connected to an external resistor 5.0 Ω. Find the terminal p.d.

Answer Details

To find the terminal p.d. (potential difference), we need to consider the concept of voltage in a circuit. Voltage is the amount of electrical energy per unit charge provided by a power source, in this case, the battery.

In this problem, we are given:

EMF (electromotive force) of the battery = 24.0 V

Internal resistance of the battery = 1.0 Ω

External resistor = 5.0 Ω

When the battery is connected to the external resistor, a current will flow in the circuit. This current is determined by Ohm's law, which states that the current flowing in a circuit is directly proportional to the voltage applied and inversely proportional to the resistance:

I = V / R

where:

I is the current flowing in the circuit

V is the voltage applied

R is the resistance of the circuit

In this case, the voltage applied is the emf of the battery, and the resistance is the sum of the internal resistance and the external resistor.

We can calculate the current flowing in the circuit:

I = 24.0V / (1.0Ω + 5.0Ω) = 24.0V / 6.0Ω = 4.0A

Now, the terminal p.d. is the voltage drop across the external resistor. We can calculate it using Ohm's law:

V = I * R

Substituting the values:

V = 4.0A * 5.0Ω = 20.0V

Therefore, the terminal p.d. is 20.0V.

When a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer because the wood is

Answer Details

When a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer because the wood is adhesive to water.

Adhesion is the attraction between different substances, in this case, water and wood. Wood is a porous material, meaning it has tiny holes or gaps in its surface. These tiny holes create a large surface area for the water droplet to interact with.

When the water droplet comes into contact with the wood, the adhesive forces between the water molecules and the wood molecules are stronger than the cohesive forces between the water molecules. This causes the water droplet to spread out, trying to maximize its contact with the wood surface.

The spreading out of the water droplet forms a thin layer because the wood surface is not completely smooth. Instead, it has irregularities and imperfections, which allow the water to seep into those gaps and spread out further.

Therefore, when a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer due to the adhesive forces between the water and the wood surface.

A relative density bottle has a mass of 19 g when empty. When it is completely filled with water, its mass is 66 g. What will be its mass if completely filled with alcohol of relative density 0.8?

Answer Details

Let mb=mass of empty bottle,

mw ${𝑚}_{𝑤}$=mass of water only and

ma ${𝑚}_{𝑎}$= mass of alcohol only
 

given; mb ${𝑚}_{𝑏}$=19g



mb ${𝑚}_{𝑏}$ + mw ${𝑚}_{𝑤}$ = 66g

mb ${𝑚}_{𝑏}$ + ma ${𝑚}_{𝑎}$ = ?

R.d=0.8

R.d=mass of alcohol

massofalcoholmassofequalvolumeofwater $\frac{𝑚𝑎𝑠𝑠𝑜𝑓𝑎𝑙𝑐𝑜ℎ𝑜𝑙}{𝑚𝑎𝑠𝑠𝑜𝑓𝑒𝑞𝑢𝑎𝑙𝑣𝑜𝑙𝑢𝑚𝑒𝑜𝑓𝑤𝑎𝑡𝑒𝑟}$

mass of equal volume of water = mw ${𝑚}_{𝑤}$=66-19=47g

0.8 = ma47 $\frac{{𝑚}_{𝑎}}{47}$


ma ${𝑚}_{𝑎}$=0.8×47 =37.6g

 mb ${𝑚}_{𝑏}$ + ma ${𝑚}_{𝑎}$ = 19+37.6=56.6g

Calculate the absolute pressure at the bottom of a lake at a depth of 32.8 m. Assume the density of the water is 1 x 10-3 kgm-3 and the air above is at a pressure of 101.3 kPa.

[Take g = 9.8 ms-2]

Answer Details

Which of the following is NOT a limitation of experimental measurements?

Answer Details

Instrument resolution is not a limitation of experimental measurements. It is the smallest change in a measured quantity that can be detected by an instrument. While instrument resolution limits the accuracy of a measurement, it is not a limitation of experimental measurements itself.

From the diagram above, if the potential difference across the resistor, capacitor and inductor are 60V, 120V and 30V respectively, the effective potential difference is

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A missile is launched with a speed of 75 ms-1 at an angle of 22° above the surface of a warship. Find the horizontal range achieved by the missile. Ignore the effects of air resistance.

[Take g = 10 ms-1]

Answer Details

A step-down transformer is used on a 2.2 kV line to deliver 110 V. How many turns are on the primary windings if the secondary has 25 turns?

Answer Details

To determine the number of turns on the primary winding of a step-down transformer, we need to understand how a transformer works and how the voltage is transformed from the primary to the secondary winding.

A transformer operates on the principle of electromagnetic induction. When an alternating current flows through the primary winding, it creates a changing magnetic field that induces a voltage in the secondary winding.

The voltage ratio between the primary and secondary windings is determined by the ratio of the number of turns in each winding. This means that if we decrease the number of turns in the secondary winding compared to the primary winding, we can reduce the voltage output.

In this case, we are given that the secondary winding has 25 turns and we want to deliver 110 V. The primary winding has a higher voltage, which is 2.2 kV (kilovolts) or 2200 V.

To determine the number of turns on the primary winding, we can set up a simple equation using the voltage ratios:

Primary voltage / Secondary voltage = Primary winding turns / Secondary winding turns

Plugging in the values we have:

2200 V / 110 V = Primary winding turns / 25 turns

Simplifying the equation:

20 = Primary winding turns / 25

To solve for the number of turns on the primary winding, we can cross multiply:

20 x 25 = Primary winding turns

Therefore, the number of turns on the primary winding is 500.

So, the correct answer is 500.

A man swung an object of mass 2 kg in a circular path with a rope 1.2 m long. If the object was swung at 120 rev/min, find the tension in the rope.

Answer Details

To find the tension in the rope, we can first use the formula for centripetal force, which is given by:
F_centripetal = (m * v^2) / r
where: - F_centripetal is the centripetal force - m is the mass of the object - v is the velocity of the object - r is the radius of the circular path
In this case, the mass of the object (m) is given as 2 kg and the radius (r) is given as 1.2 m.
Now, to find the velocity (v), we need to convert the given value of 120 rev/min to m/s.
Here's how we can do that:
1. First, convert the revolutions per minute (rev/min) to revolutions per second (rev/s) by dividing by 60 (since there are 60 seconds in a minute):
120 rev/min = 120/60 rev/s = 2 rev/s
2. Next, we need to convert the revolutions per second to the linear velocity in meters per second (m/s). To do this, we need to find the circumference of the circular path.
The circumference of a circle is given by the formula:
C = 2πr where r is the radius of the circular path.
Substituting the value of the radius (r = 1.2 m) into the formula, we have:
C = 2π * 1.2 = 2.4π Now, to find the linear velocity (v), we can multiply the circumference (C) by the number of revolutions per second (2 rev/s):
v = C * rev/s = 2.4π * 2 = 4.8π m/s
Now that we have the values of m (2 kg) and v (4.8π m/s), we can substitute them into the centripetal force formula to find the tension in the rope:
F_centripetal = (m * v^2) / r = (2 * (4.8π)^2) / 1.2
Simplifying further:
F_centripetal = (2 * 23.04π^2) / 1.2
F_centripetal = 38.4π^2
Finally, to get a numerical value for the tension in the rope, we can approximate the value of π to 3.14 and calculate the centripetal force:
F_centripetal ≈ 38.4 * 3.14^2 ≈ 379 N
Therefore, the tension in the rope is approximately 379 N.
Therefore, the correct answer is 379.

A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire.

[Take g = 10 ms-2]

Answer Details

A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.

Answer Details

T=800N; I=50cm=0.5m,

m=10g=0.01kg

fundamental freq: fo ${\mathrm{<br>}}_{}$ =?

fo ${\mathrm{<br>}}_{}$ = 121√Tμ $\frac{1}{21}<br>$

μ =m1 $\frac{\mathrm{<br>}}{}$=0.010.5 $\frac{0.01}{0.5}$

⇒ fo ${\mathrm{<br>}}_{}$ =12×0.5 $\frac{1}{2\times 0.5}$√8000.02 $\frac{800}{0.02}$

                  fo ${\mathrm{<br>}}_{}$  ⇒√ 40,000

⇒1st overtone = 2fo ${\mathrm{<br>}}_{}$ =2×200 = 400Hz

⇒2nd overtone =3fo ${\mathrm{<br>}}_{}$ =3×200=600Hz

∴3rd over tone= 4fo ${\mathrm{<br>}}_{}$  =4×200=800Hz

How much net work is required to accelerate a 1200 kg car from 10 ms-1 to 15 ms-1

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What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from −10oC to 10oC ?

[specific latent heat of fusion of ice = 3.34 x 105  Jkg−1, Specific heat capacity of water = 4200 Jkg−1 k−1

Specific heat capacity of ice = 2100 Jkg−1k−1

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In the diagram above, if the south poles of two magnets stroke a steel bar, the polarities at X and Y will respectively be

Answer Details

The polarities at X and Y would be north and north.

Name the type of equilibrium for each position of the ball

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To determine the type of equilibrium for each position of the ball, we need to understand what each type of equilibrium means. 1. **Unstable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position. In other words, the system is "unstable" and will not return to its original position on its own. 2. **Neutral equilibrium**: This occurs when a small disturbance or change in the system does not cause the object to move away from its equilibrium position. The system remains in its new position without any tendency to return to its original position. 3. **Stable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position, but the system has a tendency to return to its original position on its own. Now, let's analyze each position of the ball: A - **Unstable equilibrium**: Suppose the ball is placed at position A. If the ball is slightly disturbed or moved from this position, it will roll away further from its original position and won't come back on its own. Hence, position A is an unstable equilibrium. B - **Stable equilibrium**: Suppose the ball is placed at position B. If the ball is slightly disturbed or moved from this position, it will oscillate back and forth but eventually come back to its original position. This indicates that position B is a stable equilibrium. C - **Neutral equilibrium**: Suppose the ball is placed at position C. If the ball is slightly disturbed or moved from this position, it will stay at the new position without any tendency to return to its original position. This identifies position C as a neutral equilibrium. Based on the explanations above, the correct answer is: A - unstable, B - stable, C - neutral.

An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is

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A 400 N box is being pushed across a level floor at a constant speed by a force P of 100 N at an angle of 30.0° to the horizontal, as shown in the the diagram below. What is the coefficient of kinetic friction between the box and the floor?

Answer Details

W = 400 N; P = 100 N; θ = 30o; μ = ?

Frictional force (Fr) = μR (where R is the normal reaction)

The forces acting along the horizontal direction are Fr and Px

∴ Pcos 30° - Fr = ma (Pcos 30° is acting in the +ve x-axis while Fr in the -ve x-axis)

⇒ 100cos 30° - μR = ma

Since the box is moving at constant speed, its acceleration is zero

⇒ 100cos 30° - μR = 0

⇒ 100cos 30o = μR ----- (i)

The forces acting in the vertical direction are W, Py and R

∴ R - Psin 30° - W = 0 (R is acting upward (+ve) while Py and W are acting downward (-ve) and they are at equilibrium)

⇒ R - 100sin 30° - 400 = 0

⇒ R = 100sin 30° + 400

⇒ R = 50 + 400 = 450 N

From equation (i)

⇒ 100cos 30° = 450μ

⇒μ=100cos30°

  N = 100cos30°450 $\frac{\mathrm{<br>}}{}$

        = μ = 0.19

A 35 kΩ is connected in series with a resistance of 40 kΩ. What resistance R must be connected in parallel with the combination so that the equivalent resistance is equal to 25 kΩ?

Answer Details

For the combination in series;

⇒R1 = 35kΩ + 40kΩ = 75kΩ

R is combined with 75kΩ in parallel to give 25kΩ

=  1Req $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   125 $\frac{\mathrm{<br>}}{}$     = 1R $\frac{\mathrm{<br>}}{}$ + 175 $\frac{\mathrm{<br>}}{}$ 

=  125 $\frac{\mathrm{<br>}}{}$     - 175 $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   3−175 $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ 

=   275 $\frac{\mathrm{<br>}}{}$   = 1R $\frac{\mathrm{<br>}}{}$ 

=   752 $\frac{\mathrm{<br>}}{}$  = R

;      R = 37.5k Ω

Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. What is the frequency of the light in fused quartz?

[Speed of light c = 3 *10^8ms-1]

Answer Details

A 200 kg load is raised using a 110 m long lever as shown in the diagram above. The load is 10m from the pivot P. If the efficiency of the the lever is 80%, find the effort E required to lift the load.

[Take g = 10ms-2]

Answer Details

To find the effort E required to lift the load, we first need to understand the concept of mechanical efficiency in levers.
A lever is a simple machine that consists of a rigid beam (lever arm) that pivots around a fixed point called the fulcrum. In this case, the fulcrum is point P.
The mechanical efficiency of a lever is defined as the ratio of the output work done (load lifted) to the input work done (effort applied). Mathematically, it can be expressed as:
Efficiency = (Output Work / Input Work) * 100%
In this problem, the load is the output work and the effort is the input work.
Given: Load = 200 kg Length of lever (distance between fulcrum and load) = 10 m Efficiency = 80% Gravitational acceleration (g) = 10 m/s^2
To calculate the effort, let's first calculate the output work:
Output Work = Load * Distance lifted
The distance lifted is equal to the length of the lever arm, which is 10 m.
Output Work = 200 kg * 10 m = 2000 kg·m
Since 1 kg·m is equivalent to 10 J (1 Joule), we can convert the units:
Output Work = 2000 kg·m * 10 J/kg·m = 20000 J
Now, let's calculate the input work:
Input Work = Effort * Distance moved by the effort
The distance moved by the effort is the length of the lever arm, which is 110 m.
Input Work = Effort * 110 m
Using the formula for mechanical efficiency, we can rewrite it as:
Efficiency = (Output Work / Input Work) * 100%
Solving for the effort:
Effort = (Output Work / (Efficiency/100)) / Distance moved by the effort
Effort = (20000 J / (80/100)) / 110 m
Simplifying the equation:
Effort = (20000 J / 0.8) / 110 m
Effort = 250 J / m
Given that g = 10 m/s^2, we know that 1 N = 1 kg·m/s^2. Therefore, we can convert the units:
Effort = (250 J / m) / (1 kg·m/s^2 / 1 N)
Effort = 250 N
Therefore, the effort E required to lift the load is 250 N.

Answer Details

On a particular hot day, the temperature is 40°C and the partial pressure of water vapor in the air is 38.8 mmHg. What is the relative humidity?

Answer Details

To calculate the relative humidity, we need to understand the concept of saturation and how much water vapor the air can hold at a given temperature.
Saturation is the point at which the air is holding the maximum amount of water vapor it can hold at a particular temperature. Once the air reaches saturation, any additional moisture will start to condense into liquid water.
The amount of water vapor that the air can hold increases with temperature. Warmer air can hold more water vapor, while cooler air can hold less.
Now, let's calculate the relative humidity using the given information:
1. Find the saturation vapor pressure at 40°C: - The saturation vapor pressure is the maximum amount of water vapor the air can hold at a specific temperature. - At 40°C, the saturation vapor pressure is approximately 55.3 mmHg.
2. Calculate the relative humidity: - Relative humidity is the ratio of the current partial pressure of water vapor to the saturation vapor pressure, expressed as a percentage. - Relative Humidity = (Partial pressure of water vapor / Saturation vapor pressure) * 100 - In this case, the partial pressure of water vapor is 38.8 mmHg and the saturation vapor pressure at 40°C is 55.3 mmHg. - Plugging in these values into the formula, we get: Relative Humidity = (38.8 mmHg / 55.3 mmHg) * 100 = 70.2%
Therefore, the relative humidity on this particular hot day is approximately 70%.
Answer: The correct option is 70.

An open-tube mercury manometer is used to measure the pressure in a gas tank. When the atmospheric pressure is 101,325 Pa
, what is the absolute pressure in Pa
 in the tank if the height of the mercury in the open tube is 25 cm higher

Answer Details

A generator manufacturing company accidentally made an AC generator instead of a DC generator. To fix this error,

Answer Details

An AC generator uses slip rings to transfer the induced current smoothly to the circuit. A DC generator uses split rings to transfer the induced current to the circuit and also convert the induced AC into pulsating DC. So, to convert an AC generator into a DC generator, the slip rings needs to be replaced with split rings.

The property of wave shown in the diagram above is?

Answer Details

The property of the wave shown in the diagram is diffraction.
Diffraction is the bending or spreading out of waves as they encounter an obstacle or pass through an opening. It occurs when waves encounter an obstacle that is comparable in size to their wavelength.
In the diagram, you can see that the wave is encountering an opening or a slit, and as a result, it is spreading out or bending around the edges of the opening. This bending or spreading out is characteristic of diffraction.
Diffraction is an important phenomenon in wave behavior and is observed in various situations, such as when sound waves pass through a doorway or when light waves pass through a narrow slit. It helps us understand how waves interact with obstacles and openings in their path.
In summary, the property of the wave shown in the diagram is diffraction, which is the bending or spreading out of waves as they encounter an obstacle or pass through an opening.