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**Question 1**
**Report**

A body was slightly displaced from its equilibrium position. Which one of the following is a condition for its stable equilibrium

**Answer Details**

The condition for stable equilibrium of a body that has been slightly displaced from its equilibrium position is "an increase in the potential energy of the body." When an object is at its equilibrium position, it has a minimum potential energy. When the object is displaced from its equilibrium position, it has a higher potential energy. For the object to be in stable equilibrium, it must be able to return to its equilibrium position after it has been displaced. If the potential energy of the object increases as it is displaced, it means that the equilibrium position is a point of stable equilibrium. This is because the object will experience a restoring force that will push it back towards its equilibrium position, as the potential energy decreases. Therefore, an increase in potential energy is a condition for a body to be in stable equilibrium after it has been slightly displaced from its equilibrium position. An increase in kinetic energy or height does not necessarily indicate stability, as it depends on the specific situation and other factors at play.

**Question 2**
**Report**

A well 1km deep is filled with a liquid of density 950kg/m3 $3$ and g = 10m/s2 $2$, the pressure at the bottom of the well is

**Answer Details**

P = Pa + ρgh = (1.00 × 105
$5$) + (950 × 10 × 1000)

P = 105
$5$ + (95 × 105
$5$) = 105
$5$(1 + 95) = 96 × 105
$5$

P = 9.6 × 106
$6$ N/m2

**Question 3**
**Report**

In a slide wire bridge, the balance is obtained at a point 25cm from one end of wire 1m long. The resistance to be tested is connected to that end and a standard resistance of 3.6Ω $\Omega $ is connected to the other end of the wire. Determine the value of the unknown resistance

**Answer Details**

R3.6=7525=13 $\frac{R}{3.6}=\frac{75}{25}=\frac{1}{3}$

3R = 3.6

R = 1.2Ω

**Question 4**
**Report**

Lamps in domestic lightings are usually in

**Answer Details**

Lamps in domestic lighting are usually connected in parallel. This means that each lamp is connected directly to the power supply, rather than being connected in a series or divergent or convergent configuration. In a parallel configuration, each lamp operates independently of the others, and if one lamp fails, the other lamps will continue to function. This is an important feature for domestic lighting, as it ensures that a single lamp failure will not leave the entire room in darkness. Additionally, in a parallel configuration, each lamp can be controlled independently, for example by a switch or dimmer, without affecting the operation of the other lamps. This allows for greater flexibility in lighting design and control. In summary, lamps in domestic lighting are usually connected in parallel because it allows for independent operation of each lamp and ensures that a single lamp failure does not affect the operation of the others.

**Question 5**
**Report**

A thermocouple thermometer is connected to a millivoltmeter which can read up to 10mV. When one junction is in ice at 0°C and the other is steam at 100°C, the millivoltmeter reads 4mV. What is the maximum temperature which this arrangement can measure

**Answer Details**

The maximum temperature which this arrangement can measure is 250°C. A thermocouple thermometer works by using the thermoelectric effect, which is the phenomenon that occurs when two dissimilar metals are joined together to form a loop and a temperature difference is established between the two junctions. This temperature difference generates a small electrical voltage, which can be measured using a millivoltmeter. The voltage generated is proportional to the temperature difference between the two junctions. In the case of the thermocouple thermometer described, one junction is in ice at 0°C and the other is steam at 100°C, and the millivoltmeter reads 4mV. This means that the voltage generated by the thermocouple is 4 millivolts, which corresponds to a temperature difference of 100°C. However, the millivoltmeter can only read up to 10mV, so the maximum temperature difference it can measure is 10mV / 4mV/°C = 250°C. This means that the maximum temperature which this arrangement can measure is 250°C.

**Question 6**
**Report**

A cone is in unstable equilibrium has its potential energy

**Answer Details**

In unstable equilibrium, potential energy decreases as the height decreases.

**Question 7**
**Report**

A supply of 400V is connected across capacitors of 3μf and 6μf in series. Calculate the charge

**Answer Details**

CT $T$ | = | C1 $1$ × C2 $2$C1 $1$ + C2 $2$ |

= | 3 × 63 + 6 |

= 189
$\frac{18}{9}$ = 2μf

Q = CV

⇒ 2 × 10−6
$-6$ × 400

⇒ 800 × 10−6
$-6$C = 8 × 10−4
$-4$C

**Question 8**
**Report**

In the molecular explanation of conduction, heat is transferred by the

**Answer Details**

In the molecular explanation of conduction, heat is transferred by the Free electrons. In metals, free electrons move randomly and collide with other particles as they gain kinetic energy. These free electrons transfer the energy to the adjacent particles, which in turn gain kinetic energy and transmit it to other adjacent particles, thus transferring heat energy from one part of the material to another. This process of heat transfer by free electrons is called conduction. Therefore, the correct option is "Free electrons."

**Question 9**
**Report**

The value of T in the figure above is

**Answer Details**

Tsin30 + Tsin30 =40

2Tsin30 = 40

Tsin30 = 40/2 = 20

T(12 $\frac{1}{2}$) = 20

T = 20 x 2 = 40N

**Question 10**
**Report**

A mass of 0.5kg is whirled in a vertical circle of radius 2m at a steady rate of 2 rev/s. Calculate the centripetal force

**Answer Details**

The centripetal force is the force that acts towards the center and keeps an object moving in a circular path. To calculate the centripetal force, we can use the following formula: f = m * v^2 / r where: - f = centripetal force - m = mass of the object (0.5 kg) - v = velocity of the object (2 rev/s * 2 * pi m/rev = 12.57 m/s) - r = radius of the circle (2 m) Plugging in the values, we get: f = 0.5 kg * 12.57 m/s^2 / 2 m f = 31.43 N Rounding to the nearest whole number, the centripetal force is 31 N. So, the closest answer from the options is **160N**.

**Question 11**
**Report**

"Sum of all forces acting on a body is zero." This condition represents equilibrium'

**Answer Details**

First condition

**Question 12**
**Report**

A train has an initial velocity of 44m/s and an acceleration of -4m/s2 $2$. Calculate its velocity after 10 seconds

**Answer Details**

The velocity of the train after 10 seconds can be calculated using the formula: v = u + at where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Substituting the given values, we get: v = 44 m/s + (-4 m/s^2) x 10 s v = 44 m/s - 40 m/s v = 4 m/s Therefore, the velocity of the train after 10 seconds is 4m/s. Answer option D is correct. Explanation: The train has an initial velocity of 44 m/s and an acceleration of -4 m/s^2. The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which means that the train is slowing down. After 10 seconds, the train's velocity decreases by 40 m/s (4 m/s^2 x 10 s) to reach a final velocity of 4 m/s.

**Question 13**
**Report**

The lower fixed part of a faulty thermometer reads 2°C while the upper fixed point is 100°C.

What is the true temperature when the thermometer reads 51°C?

**Answer Details**

Since the thermometer is faulty, it is not measuring the temperature accurately. To find the true temperature, we need to determine the extent of the error in the thermometer. We can do this by comparing the difference between the lower fixed point and the reading with the difference between the upper fixed point and the true temperature. Since the lower fixed point reads 2°C and the upper fixed point reads 100°C, and the thermometer reading is 51°C, we can calculate the error as follows: True temperature = (51°C - 2°C) / (51°C - 2°C) * (100°C - 51°C) + 51°C = 50°C So, the true temperature when the thermometer reads 51°C is 50°C, which is option B.

**Question 14**
**Report**

A ray of light passes through the centre of curvature of a concave mirror and strikes the mirror. At what angle is the ray reflected?

**Answer Details**

When a light ray passes through the center of curvature of a concave mirror and strikes the mirror, the reflected ray will be reflected back on itself, creating an angle of 0 degrees. Therefore, the correct answer is 0o.

**Question 15**
**Report**

Gases conduct electricity under

**Answer Details**

Gases conduct electricity under low pressure and high voltage

**Question 16**
**Report**

In which of the points labelled A, B, C, D and E on the conductor shown would electric charge tend to concentrate most

**Answer Details**

- Charge are mostly concentrated at the outermost part of a hollow conductor

- Charge are also mostly concentrated at the pointed ends or places with high density point.

**Question 17**
**Report**

Which of the following statements is/are correct for a freely falling body?

I. the total is entirely kinetic

II. the ratio of potential energy to kinetic energy is constant

III. the sum of potential and kinetic energy is constant

**Answer Details**

The correct answer is "III only". A freely falling body is one that is falling under the influence of gravity and experiences no other force or constraint. In this situation, the total energy of the body is conserved, meaning that the sum of its potential and kinetic energy remains constant. The potential energy of a body is directly proportional to its height above the ground, and its kinetic energy is directly proportional to its velocity. As the body falls, its potential energy decreases and its kinetic energy increases, but the total energy remains constant. Statement III is correct because the sum of potential and kinetic energy is indeed constant for a freely falling body. Statement I is incorrect because the body has both potential and kinetic energy, so the total energy is not entirely kinetic. Statement II is incorrect because the ratio of potential energy to kinetic energy is not constant for a freely falling body, as both are changing as the body falls.

**Question 18**
**Report**

The part of the human eye that does similar work as the diaphragm of a camera lens is the

**Answer Details**

The part of the human eye that does similar work as the diaphragm of a camera lens is the iris. The iris is the colored part of the eye and is responsible for controlling the amount of light that enters the eye. Just like the diaphragm in a camera lens, the iris can adjust its size to allow more or less light into the eye. This helps to regulate the amount of light reaching the retina, which is responsible for sensing light and transmitting the image to the brain.

**Question 19**
**Report**

A vibrator causes water ripples to travel across the surface of a tank. The wave travels 50cm in 2s and the distance between successive crests is 5cm. Calculate the frequency of the vibrator

**Answer Details**

The frequency of the vibrator can be calculated using the formula: frequency = speed / wavelength where speed is the speed of the wave, and wavelength is the distance between successive crests. In this case, we are given that the wave travels 50cm in 2s, which means the speed of the wave is: speed = distance / time = 50cm / 2s = 25cm/s We are also given that the distance between successive crests is 5cm, which is the wavelength. Therefore, the frequency of the vibrator is: frequency = speed / wavelength = 25cm/s / 5cm = 5Hz So the correct answer is 5Hz.

**Question 20**
**Report**

Which of the following equations is the correct definition of the reactance of an indicator L?

**Answer Details**

The correct definition of the reactance of an inductor L is: Reactance = (Amplitude of voltage) ÷ (Amplitude of current) The reactance of an inductor is a measure of the opposition offered by the inductor to the flow of alternating current (AC). It is denoted by the symbol Xl and is measured in ohms. When AC flows through an inductor, a magnetic field is generated around the inductor, which opposes any changes in the current flowing through it. This opposition to the flow of current is called reactance. The reactance of an inductor depends on its inductance, frequency of the AC signal, and the amplitude of the AC signal. However, the reactance of an inductor is directly proportional to the frequency of the AC signal and the inductance of the inductor. The reactance of an inductor is also affected by the amplitude of the AC signal, but this effect is not as significant as the other two factors. is the correct definition of the reactance of an inductor, as it expresses the ratio of the amplitude of voltage to the amplitude of current, which is a common way to define reactance. is incorrect, as it represents the power delivered by the AC signal, not the reactance. and are also incorrect, as they involve squaring either the amplitude of current or the amplitude of voltage, which is not a valid method of calculating reactance. Therefore, the correct option is.

**Question 21**
**Report**

During the transformation of matter from the solid to the liquid state, the heat supplied does not produce temperature increase because

**Answer Details**

When a solid is heated to its melting point, the heat supplied is used to overcome the intermolecular forces holding the molecules in a fixed position, resulting in the breaking of these bonds. As a result, the solid transforms into a liquid without any change in temperature. This is because the heat energy supplied is used in breaking the bonds between molecules rather than increasing the kinetic energy of the molecules, which is what causes an increase in temperature. Therefore, the correct option is: "all the heat is used to break the bonds holding the molecules of the solid together."

**Question 22**
**Report**

The Earth's magnetic equator passes through Jos in Nigeria. At Jos, the

**Answer Details**

The Earth has a magnetic field that is generated by the movement of molten iron in its core. The magnetic field has different properties at different locations on the Earth's surface. The magnetic equator is an imaginary line on the Earth's surface where the inclination or tilt of the Earth's magnetic field is zero, meaning that the magnetic field lines are parallel to the Earth's surface. At Jos, Nigeria, the Earth's magnetic equator passes through, which means that the angle of inclination or dip of the Earth's magnetic field is zero. Therefore, the correct answer is that the angle of dip is zero. This means that a magnetic needle suspended by a thread or placed on a horizontal surface would remain horizontal and not point downwards or upwards, as it would at other locations on the Earth's surface. This makes Jos an important location for studying the Earth's magnetic field and for conducting experiments related to magnetism.

**Question 23**
**Report**

A boy pushes a 500kg box along a floor with a force of 2000N. If the velocity of the box is uniform, the co-efficient of friction between the box and the floor is

**Answer Details**

The coefficient of friction is a measure of the amount of friction between two surfaces. It is represented by the symbol "μ" and is a dimensionless quantity. The coefficient of friction between two surfaces depends on the nature of the surfaces in contact and the force pressing them together. In this problem, the boy is pushing the box with a force of 2000N. If the box is moving with a uniform velocity, then the force of friction acting on the box is equal and opposite to the pushing force applied by the boy. We can calculate the force of friction using the formula: frictional force = coefficient of friction x normal force where the normal force is the force exerted by the floor on the box in a direction perpendicular to the floor. Since the box is not moving up or down, the normal force is equal to the weight of the box. The weight of the box can be calculated using the formula: weight = mass x gravity where mass is the mass of the box and gravity is the acceleration due to gravity (9.8 m/s^2). So, the weight of the box is: weight = 500 kg x 9.8 m/s^2 = 4900 N The force of friction is equal to the pushing force of 2000N, so we can set these two equal to each other and solve for the coefficient of friction: frictional force = 2000N coefficient of friction x normal force = 2000N coefficient of friction x 4900N = 2000N coefficient of friction = 2000N / 4900N = 0.408 So, the coefficient of friction between the box and the floor is approximately 0.4. Therefore, the correct answer is 0.4.

**Question 24**
**Report**

The limiting frictional force between two surfaces depends on

I. the normal reaction between the surfaces

II. the area of surface in contact

III. the relative velocity between the surfaces

IV. the nature of the surfaces

**Answer Details**

- Friction depends on the nature of the surfaces in contact

- Solid friction is independent of the area of the surfaces in contact and the relative velocity between the surfaces.

**Question 25**
**Report**

Calculate the velocity ratio of a screw jack of pitch 0.2cm if the length of the tommy bar is 23cm

**Answer Details**

P = 0.2cm, L = r = 23cm

VR | = | 2?rP | = | 2?LP | = | 2?×230.2 | = | 230? |

**Question 26**
**Report**

When water is boiling, it

**Answer Details**

When water is boiling, it changes from a liquid state to a gaseous state called steam. This happens when the water is heated to its boiling point, which is when it reaches a temperature of 100 degrees Celsius (212 degrees Fahrenheit) at sea level. As the water is heated, it absorbs energy and the molecules start to move faster and faster, eventually reaching a point where they escape into the air as steam. The temperature of the water during boiling does not change, as all the energy is being used to break the bonds between the water molecules rather than increasing the temperature. Therefore, the options "gets hotter," "increase in mass," and "decreases in mass" are not correct when describing what happens when water is boiling.

**Question 27**
**Report**

Any line or section taken through an advancing wave in which all the particles are in the same phase is called the

**Answer Details**

The answer is: wave front. A wave front is any imaginary line or surface that connects all points of a wave that are in the same phase, meaning they are at the same point in their cycle. In other words, it is a line or surface that separates the points of a wave that are in-phase from those that are out-of-phase. For example, consider the ripples on the surface of a pond when a stone is thrown in. The wave fronts are the concentric circles that emanate from the point where the stone entered the water. All points along a given circle are in-phase, meaning the water molecules at those points are at the same point in their oscillation cycle. In summary, a wave front is a line or surface that separates points in a wave that are in-phase from those that are out-of-phase.

**Question 28**
**Report**

The mass of a nucleus is the

**Answer Details**

The mass of a nucleus is the total number of its protons and neutrons. The protons and neutrons are the subatomic particles that make up the nucleus of an atom. The mass of an atom is mostly concentrated in its nucleus, and the electrons orbiting the nucleus have a much smaller mass. Therefore, the mass of an atom is mostly determined by the number of protons and neutrons in its nucleus. The number of protons determines the element, and the number of neutrons can vary, resulting in isotopes of that element.

**Question 29**
**Report**

According to kinetic molecular model, in gases

**Answer Details**

According to the kinetic molecular model, in gases, the molecules are very fast apart and occupy all the space made available. This means that gas molecules are in constant random motion and they move freely in all directions without any regular arrangement. They collide with each other and with the walls of the container, exerting pressure. The temperature of the gas is related to the average kinetic energy of the gas molecules. The higher the temperature, the faster the gas molecules move, and the higher the kinetic energy.

**Question 30**
**Report**

The lead-acid accumulator consists of

**Answer Details**

- the positive pole is lead peroxide (PbO2
$2$)

- the negative pole is head

- the electrolyte is H2
$2$SO4

**Question 31**
**Report**

The angular dispersion of a prism depends on

**Answer Details**

Dispersion is due to different refractive indices speeds and wavelengths.

**Question 32**
**Report**

A body moves in SHM between two point 20m on the straight line Joining the points. If the angular speed of the body is 5 rad/s. Calculate its speed when it is 6m from the center of the motion.

**Answer Details**

From two parts 20m apart

a = 10m, x = 6m, A = 5

V = ω√A2−X2
$\sqrt{{A}^{2}-{X}^{2}}$ = 5√102−62
$\sqrt{{10}^{2}-{6}^{2}}$ = 40m/s

**Question 33**
**Report**

When two objects A and B are supplied with the same quantity of heat, the temperature change in A is obtained to be twice that of B. The mass of P is half that of Q. The ratio of the specific heat capacity of A to B is

**Answer Details**

θA = 2θB $B$,

mA $A$ | = | 12 | mB $B$ |

H = MCθ

mA
$A$cA
$A$θA
$A$ = mB
$B$cB
$B$θB
$B$

( 1/2 mB
$B$)CA
$A$ (2θB
$B$) = mB
$B$cB
$B$θB
$B$

CA $A$CB $B$ | = | 11 |

⇒ 1 : 1

**Question 34**
**Report**

Which of these is observed when air is pumped out of a discharge tube without lowering its pressure

**Answer Details**

Conduction takes places in gases when air is pumped out of a discharged tube under reduced pressure.

**Question 35**
**Report**

Electrons were discovered by

**Answer Details**

Electrons were discovered by J.J. Thompson. In the late 19th century, he performed a series of experiments using cathode ray tubes, which are glass tubes containing low-pressure gas and electrodes. By applying high voltage, he observed a beam of negatively charged particles traveling from the negative electrode to the positive electrode. He concluded that these particles, which he called "corpuscles," were fundamental units of negative charge and later were renamed electrons. This discovery led to the development of the modern understanding of atomic structure and the electron's role in it.

**Question 36**
**Report**

When blue and green colours of light are mixed, the resultant colour is

**Question 37**
**Report**

A single force which produces the same effect as a set of forces acting together at a point is known as the

**Answer Details**

The single force which produces the same effect as a set of forces acting together at a point is known as the "resultant". In other words, the resultant is the net force that results from combining all the individual forces acting on an object. It represents the combined effect of all the forces acting on the object and is the force that would produce the same motion as the original set of forces acting together. Therefore, when solving problems in physics, it is often useful to find the resultant force in order to determine the overall effect of multiple forces on an object.

**Question 38**
**Report**

The diagram shows four positions of the bob of a simple pendulum. At which of these positions does the bob have maximum kinetic energy and minimum potential energy

**Answer Details**

At position 1, the bob of the simple pendulum has the maximum potential energy and zero kinetic energy. At position 4, the bob has the maximum kinetic energy and minimum potential energy. To understand this, we need to know that the energy of a simple pendulum is converted back and forth between kinetic energy and potential energy as it swings back and forth. When the bob is at its highest point (position 1), it has the maximum potential energy because it is farthest from the ground and has the most potential to move downward. At this point, the bob has zero kinetic energy because it is momentarily at rest. As the bob swings downward towards the equilibrium point, it gains speed and its potential energy is converted to kinetic energy. At the equilibrium point (position 2), the bob has equal amounts of kinetic and potential energy. As the bob continues to move downward, its potential energy decreases and its kinetic energy increases. At position 3, the bob has minimum potential energy and some amount of kinetic energy. At the lowest point of its swing (position 4), the bob has maximum kinetic energy because it is moving at its fastest speed. At this point, the bob has minimum potential energy because it is closest to the ground and has the least amount of potential to move downward. So, to summarize, the bob has maximum potential energy at position 1, equal amounts of kinetic and potential energy at position 2, minimum potential energy at position 3, and maximum kinetic energy at position 4.

**Question 39**
**Report**

The statement 'Heat lost by the hot body equals that gained by the cold one' is assumed when determining specific that heat capacity by the method of mixtures. Which of the following validates the assumption?

I. Lagging the Calorimeter

II. Ensuring that only S.I units are used

III. Weighing the calorimeter, the lid and the stirrer.

**Answer Details**

The assumption 'Heat lost by the hot body equals that gained by the cold one' is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one system to another. Thus, to validate this assumption, it's important to have a well-designed and insulated calorimeter so that as little heat as possible is lost to the environment. This is accomplished by lagging the calorimeter (Option I). Additionally, using the correct units (Option II) helps ensure that the energy transfer is accurately calculated and reported. Weighing the calorimeter, the lid, and the stirrer (Option III) is important for accurately measuring the amount of heat transferred, but by itself is not enough to validate the assumption. Therefore, the correct answer is "I and III only".

**Question 40**
**Report**

Ripple in a power supply unit is caused by

**Answer Details**

The correct option is "Using a zener diode" as fluctuation of d.c signal results from the rectification of a.c to d.c.

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